selfemp-bayesian.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0",
   "metadata": {
    "tags": [
     "Overview"
    ]
   },
   "source": [
    "# Self employment effect -- Bayesian take\n",
    "\n",
    "## Response Model\n",
    "\n",
    "How well can we predict outcomes $Y$ conditional on treatment $T$ and other covariates $Z$?\n",
    "\n",
    "### Treatent variables\n",
    "\n",
    "   - **reduhl**\tCompleted re-education based on highest level of attainment\n",
    "   - **redudl**\tCompleted re-education based on detailed qualifications\n",
    "   - **redufl**\tCompleted re-education using highest lvl and detailed qualifications.\n",
    "\n",
    "### Outcome variables\n",
    "   - Self employed in 2019 -- **chesefin** \n",
    "   \n",
    "#### Columns explicitly excluded\n",
    "   - **xwaveid** (unique identifier)\n",
    "   - **p_rcom*** (timing of completion of re-education, proxies treatment) TODO think about how we would include this\n",
    "   - **p_cotrl** (first avail 2003)\n",
    "   - **p_rdf*** (first avail 2012)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1",
   "metadata": {
    "tags": [
     "hide_cell"
    ]
   },
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "from dataclasses import dataclass, fields\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.discrete.discrete_model import Logit, Probit\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import jax.numpy as jnp\n",
    "import numpyro as pyro\n",
    "import numpyro.distributions as dist\n",
    "from numpyro.infer import MCMC, NUTS\n",
    "from jax import random\n",
    "from jax.scipy.special import expit, erf\n",
    "\n",
    "from scipy.stats import norm, mstats\n",
    "from sklearn.model_selection import KFold, StratifiedKFold, GridSearchCV\n",
    "from sklearn.metrics import balanced_accuracy_score, accuracy_score, log_loss\n",
    "from sklearn.linear_model import LogisticRegressionCV\n",
    "from sklearn.base import BaseEstimator\n",
    "from sklearn.kernel_approximation import Nystroem\n",
    "\n",
    "from lightgbm import LGBMClassifier\n",
    "\n",
    "from reed import drop_missing_treatment_or_outcome, Model, transform_outcome\n",
    "from direct_regression import seperate_and_transform_data, print_unconditional_effects\n",
    "\n",
    "pyro.enable_x64()\n",
    "%matplotlib inline"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2",
   "metadata": {},
   "source": [
    "## Analysis Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3",
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "exclude_patterns = [\n",
    "    '^reduhl$', '^rehllt$', '^redudl$', '^redufl$', '^redllt$', '^refllt$',\n",
    "    '^rlwage$', '^mh$', '^mhbm$', '^wkhr$', '^y_', '^p_rcom','^p_rdf','^p_cotrl',\n",
    "    '^xwaveid$','p_rcom18','^aedcq', '^abnfsty','^aedcqfpt','^aedqstdy'\n",
    "]\n",
    "data_load_func = lambda filepath: pd.read_csv(filepath, index_col='xwaveid')\n",
    "\n",
    "#configuration_name = 'default'\n",
    "outcome = 'chsefin'\n",
    "treatment = 'redufl'\n",
    "test = False\n",
    "data_file = Path(\"~/Code/re-education/data/all_lasso_selected_100_restricted.csv\")\n",
    "outc_file = Path(\"~/Code/re-education/data/transition_self_employed.csv\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "4",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5",
   "metadata": {
    "tags": [
     "hide_cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dropped 0 rows missing treatment or outcome.\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = data_load_func(data_file)\n",
    "target = data_load_func(outc_file)\n",
    "data = data.join(target)\n",
    "drop_missing_treatment_or_outcome(data, treatment, outcome)\n",
    "data[outcome] = transform_outcome(data[outcome], False, False)\n",
    "\n",
    "    \n",
    "plt.hist(data[outcome])\n",
    "plt.xlabel(outcome)\n",
    "plt.ylabel(\"count\")\n",
    "plt.title(\"Distribution of outcomes\");"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6",
   "metadata": {},
   "source": [
    "## Prepare data for modeling\n",
    "\n",
    "- split into treated/control\n",
    "- impute missing values and scale\n",
    "- separate features from outcomes&treatments\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control data dimensions:  (4043, 91)\n",
      "Treated data dimensions: (1398, 91)\n"
     ]
    }
   ],
   "source": [
    "from direct_regression import seperate_and_transform_data\n",
    "X0, X1, y0, y1, X, y, t, features = seperate_and_transform_data(data, treatment, outcome)\n",
    "print(\"Control data dimensions: \", X0.shape)\n",
    "print(\"Treated data dimensions:\", X1.shape)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8",
   "metadata": {},
   "source": [
    "## Compute unconditional/unadjusted estimate of treatment effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion Treated:26%\n",
      "Average outcome under Control:0.05±0.00\n",
      "Average outcome under Treatment:0.08±0.01\n",
      "Unadjusted treatment estimate (log-odds) 0.46\n",
      "Unadjusted treatment estimate 0.03\n"
     ]
    }
   ],
   "source": [
    "print_unconditional_effects(data, treatment, y0, y1, logodds=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "10",
   "metadata": {},
   "source": [
    "## Statsmodels\n",
    "\n",
    "### GLM S-learner -- Logit and Probit models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "11",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probit model\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.190554\n",
      "         Iterations: 131\n",
      "         Function evaluations: 132\n",
      "         Gradient evaluations: 132\n",
      "Marginal effect: 0.0131 [0.0000, 0.0263]\n",
      "\n",
      "Logit model\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.190973\n",
      "         Iterations: 250\n",
      "         Function evaluations: 251\n",
      "         Gradient evaluations: 251\n",
      "Marginal effect: 0.0122 [-0.0009, 0.0253]\n"
     ]
    }
   ],
   "source": [
    "Xt = np.hstack((t[:, np.newaxis], X))\n",
    "Xt = pd.DataFrame(data=Xt, columns=[\"treatment\"] + features)\n",
    "#Xt[\"treatment\"] = Xt[\"treatment\"].astype(\"category\")\n",
    "tind = list(Xt.columns).index(\"treatment\")\n",
    "\n",
    "print(\"Probit model\")\n",
    "glmp = Probit(y, sm.add_constant(Xt))\n",
    "resp = glmp.fit(maxiter=500, method=\"bfgs\")\n",
    "mresp = resp.get_margeff()\n",
    "ate_glmp = mresp.margeff[tind]\n",
    "ci_glmp = mresp.conf_int()[tind]\n",
    "print(f\"Marginal effect: {ate_glmp:.4f} [{ci_glmp[0]:.4f}, {ci_glmp[1]:.4f}]\")\n",
    "\n",
    "print(\"\\nLogit model\")\n",
    "glml = Logit(y, sm.add_constant(Xt))\n",
    "resl = glml.fit(maxiter=500, method=\"bfgs\")\n",
    "mresl = resl.get_margeff()\n",
    "ate_glml = mresl.margeff[tind]\n",
    "ci_glml = mresl.conf_int()[tind]\n",
    "print(f\"Marginal effect: {ate_glml:.4f} [{ci_glml[0]:.4f}, {ci_glml[1]:.4f}]\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "5b65c0b7",
   "metadata": {},
   "source": [
    "## Train a propensity score model\n",
    "\n",
    "This should help with bias in estimating treatment effects with Bayesian models.\n",
    "\n",
    "See:\n",
    "\n",
    "[Hahn, P.R., Murray, J.S. and Carvalho, C.M., 2020. Bayesian regression tree models for causal inference: Regularization, confounding, and heterogeneous effects (with discussion). Bayesian Analysis, 15(3), pp.965-1056.](https://projecteuclid.org/journals/bayesian-analysis/volume-15/issue-3/Bayesian-Regression-Tree-Models-for-Causal-Inference--Regularization-Confounding/10.1214/19-BA1195.pdf)\n",
    "\n",
    "\n",
    "For more information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3de1ef0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_prop = LogisticRegressionCV(max_iter=500)\n",
    "nonlin_prop = GridSearchCV(\n",
    "    LGBMClassifier(),\n",
    "    param_grid={\"learning_rate\": [1e-3, 1e-2, 5e-2, 0.1, 0.5]},\n",
    "    scoring=\"neg_log_loss\",\n",
    "    n_jobs=-1\n",
    ")\n",
    "\n",
    "\n",
    "@dataclass\n",
    "class ScoreMap:\n",
    "    sfn: callable\n",
    "    sres: list\n",
    "        \n",
    "    def __init__(self, sfn):\n",
    "        self.sfn = sfn\n",
    "        self.sres = []\n",
    "\n",
    "        \n",
    "@dataclass\n",
    "class Scores:\n",
    "    accuracy: ScoreMap\n",
    "    baccuracy: ScoreMap\n",
    "    logloss: ScoreMap\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.accuracy = ScoreMap(sfn=accuracy_score)\n",
    "        self.baccuracy = ScoreMap(sfn=balanced_accuracy_score)\n",
    "        self.logloss = ScoreMap(sfn=log_loss)\n",
    "\n",
    "        \n",
    "@dataclass\n",
    "class ModelMap:\n",
    "    model: BaseEstimator\n",
    "    propensity: np.ndarray\n",
    "    scores: Scores\n",
    "    \n",
    "    def __init__(self, model):\n",
    "        self.model = model\n",
    "        self.propensity = np.zeros(len(t))  # zeros_like becomes immutable?\n",
    "        self.scores = Scores()\n",
    "        \n",
    "    def set_ps(self, ind, p):\n",
    "        self.propensity[ind] = p\n",
    "        \n",
    "\n",
    "pmodels = {\n",
    "    \"logistic\": ModelMap(model=linear_prop),\n",
    "    \"gbc\": ModelMap(model=nonlin_prop)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5e27d0cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round 0\n",
      "Round 1\n",
      "Round 2\n",
      "Round 3\n",
      "Round 4\n"
     ]
    }
   ],
   "source": [
    "for i, (tr_ind, ts_ind) in enumerate(StratifiedKFold(n_splits=5, shuffle=True).split(X, t)):\n",
    "    t_tr, t_ts = t[tr_ind], t[ts_ind]\n",
    "    X_tr, X_ts = X[tr_ind], X[ts_ind]\n",
    "    \n",
    "    print(f\"Round {i}\")\n",
    "    for name, props in pmodels.items():\n",
    "        props.model.fit(X_tr, t_tr)\n",
    "        p = props.model.predict_proba(X_ts)[:, 1]\n",
    "        t_hat = (p > 0.5).astype(int)\n",
    "        \n",
    "        props.scores.logloss.sres.append(props.scores.logloss.sfn(t_ts, p))\n",
    "        props.scores.baccuracy.sres.append(props.scores.baccuracy.sfn(t_ts, t_hat))\n",
    "        props.scores.accuracy.sres.append(props.scores.accuracy.sfn(t_ts, t_hat))\n",
    "        \n",
    "        props.set_ps(ts_ind, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "009c6bbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "logistic-accuracy: 0.7432 (0.0008)\n",
      "logistic-baccuracy: 0.5076 (0.0119)\n",
      "logistic-logloss: 0.5225 (0.0141)\n",
      "gbc-accuracy: 0.7390 (0.0052)\n",
      "gbc-baccuracy: 0.5483 (0.0082)\n",
      "gbc-logloss: 0.5157 (0.0080)\n"
     ]
    }
   ],
   "source": [
    "for name, props in pmodels.items():\n",
    "    for f in fields(props.scores):\n",
    "        score = getattr(props.scores, f.name)\n",
    "        smean, sstd = np.mean(score.sres), np.std(score.sres, ddof=1)\n",
    "        print(f\"{name}-{f.name}: {smean:.4f} ({sstd:.4f})\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "92f77633",
   "metadata": {},
   "outputs": [],
   "source": [
    "# There is not much difference in model performance, so go with logistic model for simplicity\n",
    "p = linear_prop.fit(X, t).predict(X)\n",
    "#p = pmodels[\"gbc\"].propensity"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "21",
   "metadata": {},
   "source": [
    "## Hierarchical Bayesian Model\n",
    "\n",
    "This model takes the following form and prior settings,\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "    \\{\\lambda_0, \\lambda_x, \\lambda_{\\pi}\\} &\\sim \\textrm{Uniform}(0, 100) \\\\\n",
    "    \\{\\lambda_t, \\lambda_{tx}\\} &\\sim \\textrm{Uniform}(0, 1000) \\\\\n",
    "    w_0 &\\sim \\mathcal{N}(0, \\lambda_0^2) \\\\\n",
    "    w_\\pi &\\sim \\mathcal{N}(0, \\lambda_\\pi^2) \\\\\n",
    "    \\mathbf{w}_x &\\sim \\mathcal{N}(0, \\lambda_x^2 \\mathbf{I}_d) \\\\\n",
    "    w_t &\\sim \\mathcal{N}(0, \\lambda_t^2) \\\\\n",
    "    \\mathbf{w}_{tx} &\\sim \\mathcal{N}(0, \\lambda_{tx}^2 \\mathbf{I}_d) \\\\\n",
    "    y_i &\\sim \\mathrm{Bernoulli}\\!\\left(\\mu(\\mathbf{x}_i, t_i, \\pi_i)\\right) \\\\\n",
    "    \\mu(\\mathbf{x}_i, t_i, \\pi_i) &= \\Phi\\!\\left(\\rho(\\mathbf{x}_i, \\pi_i) + t_i \\cdot \\tau(\\mathbf{x}_i)\\right) \\\\\n",
    "    \\tau(\\mathbf{x}_i) &= \\mathbf{w}_{tx}^\\top\\mathbf{x}_i + w_t\\\\\n",
    "    \\rho(\\mathbf{x}_i, \\pi_i) &= w_0 + w_\\pi \\pi_i + \\mathbf{w}_x^\\top\\mathbf{x}_i\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "Where $\\Phi(z)$ is a logistic or Normal CDF (inverse probit) function. This explicitly models and interaction term, and can automatically regularise this term. This effectively allows the model to interpolate between an S and T-learner.\n",
    "\n",
    "Since this is no longer a linear model, we have to rely on *partial effects* to compute the ATE,\n",
    "$$\n",
    "\\begin{align}\n",
    "    \\hat{\\textrm{ATE}} = \\sum_{i=1}^n \\mu(\\mathbf{x}_i, 1, \\pi_i) - \\mu(\\mathbf{x}_i, 0, \\pi_i).\n",
    "\\end{align}\n",
    "$$\n",
    "See [2] equation 17.8 for more detail. Unfortunately, we lose the nice linear separation between the prognostic and treatment models. \n",
    "\n",
    "For ideas about choice of prior, we should refer to:\n",
    "\n",
    "[1] Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian analysis, 1(3), 515-534.\n",
    "\n",
    "[2] Wooldridge, J.M., 2015. Introductory econometrics: A modern approach. Cengage learning."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "22",
   "metadata": {},
   "source": [
    "### Set up the model\n",
    "\n",
    "Probability transformation (inverse link) functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "48ed5f33",
   "metadata": {},
   "outputs": [],
   "source": [
    "def iprobit(x):\n",
    "    p = 0.5 * (1 + erf(x / jnp.sqrt(2)))\n",
    "    return p\n",
    "    \n",
    "\n",
    "def ilogit(x):\n",
    "    p = expit(x)\n",
    "    return p\n",
    "\n",
    "\n",
    "def icloglog(x):\n",
    "    p = 1 - jnp.exp(- jnp.exp(x))\n",
    "    return p\n",
    "\n",
    "\n",
    "TFM_FUNCTION = ilogit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ef970554",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    },
    {
     "data": {
      "image/png": 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EMnv2D36MugaZJhzZDJu/8X6lby29vUUn6DgS2g+HxP7eobAilaBkRESkDCk5KYyfM57Mgky6NOvC6yNeJ8wRVvGOZXB7DJ6fs403F+wGoPcZTXltbC/imoTUj2fyHD8Av3wKG2bC0R2/rbc6oN0wOHO0NwlpmhSoCKWeUzIiIvI7bsPN/QvuJy0vjXZN2jFj5AyigqrWxJCZ6+TP/1rDij3e+Uj+OLgtD13YGYetjo+QcebB1v/C+o9h9wJKZiy1BUOHEdD1cm8SEhodyCilgVAyIiLyO+9ufJeNGRuJdEQyY8QMmoVUbXTH0ZxCrn9nBVtTs4kItvPcH7px0Tnxfo7Wz47tg1Vvw9p/QsHx39YnDYEeY6HLpd5ZSEX8SMmIiMhJNh/dzIwNMwCYnDyZ+IiqJQ/p2YVc/85ytqflEBMZzMe3JdMxto7+J26a3hEwK96E7T+AWfTk8+g20OMG6D5GTTBSo5SMiIgUKfQU8sjiR3CbbkaeMZJL2l1SpeMcyS5g7Nsr2Hkkh9ioYP49vj/tWtbBzpyG4U0+Fj4Ph06amLLdcEj+E3Qc5X0Am0gNUzIiIlLk1XWvsvP4TpqFNOPR/o9WaXr3I1kFXPf2cnal5xIXFcK/b+9P2xZ17KGXhgc2fw0L/wFHNnnXOcKgx/XQ73ZoeWZAw5PGp473oGq4hg0bxn333ee34z3xxBP06NHDb8cTaWzWpK3hw00fAvDEgCeq1E8ku8DF9e+sYFd6LglNQpj5pzqWiJgmbJsNbwyEL271JiJBkTDkL3DvRrj4BSUiEhC6M9JATJo0ibvvvrvk/S233MLx48f5+uuvAxeUSD2R787nkcWPYGJyRYcrGN5meMU7/Y5hmNw3cwM7ippmPr19AG2aV20ocI1IWQtzH/dO0Q4QEg3974Tk2yG0aUBDE1Ey0kBEREQQEVEH26RF6oF/b/03KTkpxIbF8mDfB6t0jJfm7eCnLWkE2a28dWOfupOInDgIc6fAr19439uCof+fYfB9GpYrdYaaaeqAY8eOcdNNN9G0aVPCwsK48MIL2bFjR6kyb7/9NomJiYSFhXHllVcybdo0oqOjS7af3EzzxBNP8OGHH/LNN99gsViwWCx6Eq/IaWQ7s3l347sA3N3zbiKCfE/qf9yUykvzvL+zf7vibLonRvszxKrxuGHZ6/BaclEiYoFu18Lda2Dkk0pEpE5peHdGTBNceYE5tyMMqtDhbdy4cezcuZNvv/2WqKgoHnzwQS666CI2b96Mw+FgyZIl3HHHHTz77LNcdtll/PTTTzz22GOnPd6kSZPYsmULWVlZvP/++wA0a6anYIqU5YNNH5DlzKJdk3ZVGj2zIy2biTPXA3DLwCSu7pPo5wirIGUtfHcPpP7ifZ+YDBc9D/HdAxuXyGk0vGTElQfPJATm3A8fgiDfOqvt2rWL7777jiVLljBw4EAAPv74YxITE/n666+5+uqreeWVV7jwwguZNGkSAGeeeSZLly7lv//9b5nHjIiIIDQ0lMLCQuLi4qpXJ5EG7Gj+Uf65+Z+A966IzcdhrCfyXYz/aDW5Tg8D2jXnkYu71ESYlefMg3lPwco3vXOFhDSBkU9Bz5vAqhvhUnfppzPAtm3bht1uJzk5uWRd8+bN6dSpE1u2bCkp069fv1L7/f69iPjunY3vkO/O56zmZ3F+m/N93v/xb35l79E8WkWH8urYnoGd4v3wBnhrGKx4w5uInHMNTFgNvW9RIiJ1XsO7M+II896hCNS5RaReOJxzmJnbZgLwf73+z+c5ReZtSeOb9YewWuDVsT1pHlH1p/lWi+GBpS/Dz38DwwURsXD569BxRGDiEamChpeMWCw+N5UEUqdOnXC73axYsaKkmebo0aNs27aNrl27lpRZtWpVqf1+//73goKC8Hg8NRO0SAMw45cZuAwX/eL6MSB+gE/7ZhW4eOSrXwG4bUg7erYJ0NDYEwfhP3+CfYu97ztfApe+DOHNAxOPSBXp3l2AtW/fnssuu4zx48ezePFiNmzYwA033ECrVq24/PLLAbj77ruZNWsW06ZNY8eOHbz55pv88MMP5f4ll5SUxC+//MK2bdvIyMioH48pF6kle07s4eudXwNVuysyddYWUrMKSGoexn0jAjRJ2J5F8OZQbyISFAGXvwZj/qVEROolJSN1wHvvvUfv3r255JJLGDBgAKZpMmvWLBwOBwCDBg1ixowZTJs2je7duzN79mzuu+8+QkJCTnvM8ePH06lTJ/r06UPLli1ZsmRJbVVHpM6bsWEGhmkwLHEY3Vv6NsJk6c4M/r3yAADPXtWN0KBafnaLacKy1+CjyyEvA+K6wR2LoOcNVRrNJ1IXNLxmmnpi/vz5GIZBVlYWTZs25aOPPiq3/Pjx4xk/fnyp9x06dCh5/8QTT/DEE0+UvG/ZsiVz5szxe9wi9d2RvCPM2ev93biz+50+7ZvndPPgf7zDZW/o34bkdrV8F8KZC9/+328TmHW7Fi6dDo7Q2o1DxM+UjNQTL7zwAiNHjiQ8PJwffviBDz/8kNdffz3QYYnUO59v/xy36aZXTC+6NPdtKO4LP27nQGY+CU1CePCCzjUU4WmcSIFPxkDaRrDaYfQz3ofa6W6INABKRuqJlStX8txzz5GdnU27du14+eWXue222wIdlki94vK4+Hzb5wBc1+U6n/bdlprNB0v3APDM/zuHyBCH3+M7rbTN8PEfICsFwmPgmg/hjIG1d36RGqZkpJ747LPPAh2CSL03Z98cjhYcJSY0xud5RZ7/cSuGCRecFcewTjE1FGEZ9i6BT6+DghPQohPc8AVEt6m984vUAiUjItJofLL1EwCu7nQ1Dmvl72ys3JPJT1uOYLNauP+CTjUV3qk2fQ3/GQ8eJyT2h+v+DWF6tIM0PEpGRKRR2JSxiV/Sf8FutfOHM/9Q6f1M02TqD97ZkMf0TaR9y1p6OvbKt2HW/YDpnT/kqnfUUVUaLA3tFZFGofiuyOik0bQIbVHp/X7clMa6/ccJddi49/yONRVeaSveglmTABP63gbXfKRERBo0JSMi0uBlFmTyw54fABjbeWyl93N7DJ77cSsAtw1pS0zU6ef28ZsVb8IP93uXB98HF70APj7AT6S+UTONiDR4X27/Epfh4uzmZ9OtZbdK7/f5moPsTs+laZiD289tV4MRFlk+A2Y/6F0ePBHOf1xDd6VRUDIiIg2a23CXPBBvbJfK3xXJd3p4ce52AO4+r2OND+W1rnoL5jzsfTPkL3DeY0pEpNFQM00dtHfvXiwWC+vXr/frcZOSkpg+fbpfjylS1y06uIi0vDSahTRjVNKoSu/3wdK9HMkupHXTUK7vX7NDadscXYBNiYg0YkpGRKRB++/u/wJwSbtLCLYFV2qfApeHdxd7Jzi7d8SZBNtrrs+GZftseux/z/tm0D1KRKRRUjIiIg1WtjOb+QfmA95kpLK+XpdCRk4hCU1CuLxHQs0EB7B/BbavbsOCidHtOhjxpBIRaZSUjASQYRi89NJLnHnmmQQHB9OmTRv+9re/lVl2wYIF9OvXj+DgYOLj43nooYdwu90l27Ozs7n++usJDw8nPj6eF198kWHDhnHvvfee9vz79+/n8ssvJyIigqioKK655hrS0tJKlfnrX/9KTEwMkZGR3HbbbTz00EP06NHDH9UXqXE/7fsJp+GkfZP2dG5WuWfJGIbJ24t2A3Dr4LY4bDX0MZm+Df49Bou7gNSo7ngumqZERBqtBpeMmKZJnisvIF+mafoU68MPP8z06dN55JFH2Lx5M5988gmxsbGnlEtJSeGiiy6ib9++bNiwgTfeeIN3332Xv/71ryVlJk6cyJIlS/j222+ZO3cuixYtYu3atac9t2EYXH755WRmZrJgwQLmzp3L7t27GTNmTEmZjz/+mL/97W88++yzrFmzhjZt2vDGG2/4VEeRQCppoml/CZZK/kf/89Yj7ErPJTLYzpi+iTUTWNYh+NdVkH8MI6EXq5MmgK0Wn3UjUsc0uNE0+e58kj9JDsi5V4xdQZgjrFJls7Ozefnll3nuuee4+eabsVqttG/fnsGDB7N3795SZV9//XUSExN59dVXsVgsdO7cmUOHDvHggw/y+OOPk5uby4cffsgnn3zC+ed7n7fx/vvvk5Bw+tvL8+bNY+PGjezZs4fERO8H7kcffcRZZ53FqlWr6Nu3L6+88gp//OMfGTduHACPP/44c+bMIScnpwpXR6R2peamsip1FQAXt7240vu9tdB7V2Rs/zY1M4LGmQufXAMnDkDzDnjG/BvP/BX+P49IPdLg7ozUF1u2bKGwsJChQ4dWquyAAQNK/WU3aNAgcnJyOHjwILt378blctGvX7+S7U2aNKFTp9M/Q2PLli0kJiaWJCIAXbt2JTo6mi1bvFNfb9u2rdQxgVPei9RVs/bMwsSkT2wf4iPiK7XPuv3HWLk3E4fNwriBbf0flGnCNxMgdSOEtYAbvoSw5v4/j0g90+DujITaQ1kxNjB/ZYTaKz9dc2iopnYWqUknj6KprOK+Ipd1b0VckxqYbXXxi7DpP2C1w5h/QtMkcLn8fx6ReqbB3RmxWCyEOcIC8lXZNmmAjh07EhoayoIFCyos26VLF5YtW1aqT8qSJUuIjIykdevWtGvXDofDwapVq0q2nzhxgu3bt5d7zAMHDnDgwIGSdZs3b+b48eN07doVgE6dOpU6JnDKe5G6aFvmNnYc24HD6mBk0shK7bPvaC6zf00FqJnZVrf/CPOe8i5f+BycMdD/5xCppxrcnZH6IiQkhAceeIApU6YQFRXFkCFDSE9PZ9OmTSX9PordeeedTJ8+nbvvvpsJEyawbds2pkyZwsSJE7FarURGRnLzzTdz//3306xZM2JiYpgyZQpWq/W0CdKIESM455xzuP7665k+fTput5s777yToUOH0qdPHwDuvvtuxo8fT58+fRg4cCAzZ87kl19+oV27WpgWW6Qavt/9PQDDEocRFRRVqX3eXbwHw4RhnVrSKS7SvwFl7IAvbwNM6H0L9P2jf48vUs8pGQmgRx99FLfbzRNPPMGhQ4eIj4/njjvuOKVcq1atmDVrFvfffz/du3enWbNm/PGPf+TRRx8tKTNt2jTuuOMOLrnkEqKionjggQc4cOAAISFl32q2WCx888033H333Zx77rlYrVYuuOACXnnllZIy119/Pbt372bSpEkUFBRwzTXXcMstt7By5Ur/XwwRP/EYHr7f401GLm5XuY6rx/OcfLbae5fQ73dFCk7Av6+DwixI7A8XPu/f44s0AEpGAshqtTJp0iSeeuoprNbSLWa/HyY8dOjQcpOAyMhIPv7445L3ubm5PPnkk9x+++0l634/SqdNmzZ888035cb42GOP8dhjj5W8HzlyJB06dCh3H5FAWp22miN5R4gKimJIqyGV2uc/a1MocBl0iY9iQDs/dig1TfjuHji6A6JaefuJ2IP8d3yRBkLJSAOxbt06tm7dSr9+/Thx4gRPPeVtm7788surfMy8vDxmzJjB6NGjsdls/Pvf/+ann35i7ty5/gpbxO+KO66OThpNkK3i//hN02TmKu9dkbH9En3q+1WhtR/Bpq+8HVav/hAiYvx3bJEGRMlIA/LCCy+wbds2goKC6N27N4sWLaJFixZVPp7FYmHWrFn87W9/o6CggE6dOvHll18yYsQIP0Yt4j8uj4t5++YBcFHbiyq1z7oDx9mWlk2Iw8plPVr5L5gjW+GHB73L5z0KiX39d2yRBkbJSAPRs2dP1qxZ49djhoaG8tNPP/n1mCI1aVXqKrJd2TQPaU7PmJ6V2mfmSu9dkYvOiadJqJ8mOXPlwxe3gjsf2g2Hgff457giDVSDG9orIo3XvP3euyLD2wzHZq34Sbs5hW6+++UQANf2beO/QH58BI5sgvCWcOWbYNVHrUh59BsiIg2CYRr878D/ADi/zfkVlPb6bsMh8pwe2rUMp29SU/8EsvlbWP2ud/nKNyHy1OdNiUhpDSYZ8fUhdVIz9H2QQPkl/RfS89OJcESQHFe551N9WtRx9dq+fuq4mp0K397tXR50L3SoXFIk0tjV+2TEZvPeinU6nQGORMA7AgfA4dATSKV2/bz/ZwCGtB6CoxJPwN1yOIsNB47jsFn4f71aVz8A04T/3gcFxyG+u7fTqohUSr3vwGq32wkLCyM9PR2Hw3HKfB11mWEYOJ1OCgoK6lXcZTFNk7y8PI4cOUJ0dHRJkihSG0zTLOkvUtkmmuLhvCO7xtIiIrj6QWz8HLbNAqsDrngDKpEQiYhXvU9GLBYL8fHx7Nmzh3379gU6HJ+Ypkl+fj6hoaH+ndsggKKjo4mLiwt0GNLI7Dy+k/3Z+wmyBlVqorMCl4f/rD0IwBh/dFzNToNZ93uXhz4IsWdV/5gijUi9T0YAgoKC6NixY71rqnG5XCxcuJBzzz23QTRrOBwO3RGRgCi+KzIgYQBhjrAKy/+4KZWsAjetokMZ0qHqc/EApzbPDL63escTaYQaRDIC3qnVT/cclrrKZrPhdrsJCQlpEMmISKD42kTz+WrvXZGr+7TGaq3mXcmNX8C279U8I1IN9bujgog0egezD7I1cytWi5VhicMqLH8ku4CluzIAuKq6HVez0+AHNc+IVJeSERGp14pH0fSO7U3TkIrnCvlhYyqGCT0So0lsVnGTTrl+nAz5x9Q8I1JNSkZEpF7ztYnmuw3eGVcv655QvRPv+h/8+iVYrHDZK2qeEamGKiUjr732GklJSYSEhJCcnFzuo+0Bpk+fTqdOnQgNDSUxMZH77ruPgoKCKgUsIlLsaP5R1h1ZB8B5iedVWD7leD6r9x3DYoGLu8VX/cTuQpg1ybvc73bvnRERqTKfk5GZM2cyceJEpkyZwtq1a+nevTujR4/myJEjZZb/5JNPeOihh5gyZQpbtmzh3XffZebMmTz88MPVDl5EGrcFBxdgYtK1eVfiIypOLv5bdFckuW0zYqOq0eF96ctwdCdExMJwfZaJVJfPyci0adMYP34848aNo2vXrsyYMYOwsDDee++9MssvXbqUQYMGMXbsWJKSkhg1ahTXXXddhXdTREQqsujgIoBKdVwFSh6Kd2l1mmiO7YWFL3iXRz8DIU2qfiwRAXwc2ut0OlmzZg2TJ08uWWe1WhkxYgTLli0rc5+BAwfyr3/9i5UrV9KvXz92797NrFmzuPHGG097nsLCQgoLC0veZ2VlAd55OVwuly8h12nFdWlIdfJVY78Gjb3+UPVr4PK4WHbI+7kzMHZghfvvycjl15Qs7FYLIzq1qNo1N01s30/C6i7ASBqCp9NlUM3vnX4GdA0acv0rWyefkpGMjAw8Hg+xsaWfQhkbG8vWrVvL3Gfs2LFkZGQwePBgTNPE7XZzxx13lNtMM3XqVJ588slT1s+ZM4ewsGr2fq+D5s6dG+gQAq6xX4PGXn/w/Rrsdu0m151LuCWc3ct3s9eyt9zysw9YABsdozwsX/BTlWKMO76G5D1zMSw2/hd6MTk//FCl45RFPwO6Bg2x/sXPK6tIjU96Nn/+fJ555hlef/11kpOT2blzJ/fccw9PP/00jz32WJn7TJ48mYkTJ5a8z8rKIjExkVGjRhEVFVXTIdcal8vF3LlzGTlyZKOd9KyxX4PGXn+o+jV4cd2LsAXOSzqPSwZcUm5Z0zR56eWlQC7jzuvGRT2r0Ezjysc+w/tHlDngbs4dfpvvxyjrsPoZaPTXoCHXv7hloyI+JSMtWrTAZrORlpZWan1aWtppn0fy2GOPceONN3Lbbd5f3HPOOYfc3Fxuv/12HnnkkTIfEBccHExw8KkPrnI4HA3uGwUNt16+aOzXoLHXH3y/BksPLQXg3DYVP05hy+EsdmfkEmS3ckG3hKpd62XTIesgRLXGNuwBbH7+fulnQNegIda/svXxqQNrUFAQvXv3Zt68eSXrDMNg3rx5DBgwoMx98vLyTkk4ip9fYpqmL6cXEQEgJSeFXSd2YbPYGBBf9mfPyYrnFhneqSVRIVX4sM9Og8XTvcsjnoCgcN+PISKn5XMzzcSJE7n55pvp06cP/fr1Y/r06eTm5jJu3DgAbrrpJlq1asXUqVMBuPTSS5k2bRo9e/YsaaZ57LHHuPTSS/VQNRGpksUHFwPQvWV3mgSXP5rFNM3qj6L539/AmQOtesPZV1XtGCJyWj4nI2PGjCE9PZ3HH3+c1NRUevTowezZs0s6te7fv7/UnZBHH30Ui8XCo48+SkpKCi1btuTSSy/lb3/7m/9qISKNysKUhQAMaT2kwrIbDp7gQGY+YUE2zu8cW2H5U6RtgnX/9C6PfgbKaFoWkeqpUgfWCRMmMGHChDK3zZ8/v/QJ7HamTJnClClTqnIqEZFSCtwFrDzsnadoSKuKk5E5m1IBGN45htAgH+/Gmib8+AiYBnS9HNr09zleEamYUnwRqVdWp62mwFNATFgMZzY9s8Lyczd7O9yP6lqFuyI7f4Ld/wNbkLeviIjUCCUjIlKvFM+6OqTVECwWS7ll92bksuNIDnarhWGdYnw7kccNcx71Lif/CZq1q0q4IlIJSkZEpN4wTZOFByvfX6T4rkhyu2Y0CfVxFM26jyB9K4Q2gyGTfI5VRCpPyYiI1Bv7svZxMOcgdqu9UkN6i5ORkV18bKJx5sH8Z73LQx+E0GgfIxURXygZEZF6Y1GKt4mmT2wfwhzlPxoiM9fJ6n2ZAIzwtb/IqncgJxWatIE+t1YpVhGpPCUjIlJvnNxfpCLztqRhmNA1PorWTX14plVBFix+0bs87EGwB1UlVBHxgZIREakX8lx5rE5bDcDg1oMrLF/SROPrXZHlb0B+JjTvCN2u9TlOEfGdkhERqRfWpK3BZbiID4+nbVTbcssWuDws2pEB+JiM5GXCsle9y8Mng63GnyUqIigZEZF6YtnhZQAMTBhY4ZDexTsyyHd5aBUdylkJPjzpe8lLUJgFsedA1yurE66I+EDJiIjUC8sOeZORAQmVH0UzoktMhYlLiexUWPGmd/m8RzTtu0gt0m+biNR5ablp7Dy+EwsW+seXPyW7xzCZt7W4v0hc5U+y6B/gzodWfeDMC6oTroj4SMmIiNR5xU00Z7c4u8Kn9K4/cIyMHCeRIXaS2zWr3AlOHITV73uXz38MKns3RUT8QsmIiNR5Sw8tBajwrgjAnKImmuGdYnDYKvkRt+QlMFxwxmBoN6yqYYpIFSkZEZE6zTANVhxeAXg7r1bkJ1+H9GanwZoPvctDH6hSjCJSPUpGRKRO25a5jcyCTMLsYXRv2b3csgcy89iVnovNauHcM1tW7gTLXgFPIbTuB23P9UPEIuIrJSMiUqcVN9H0i+uHw1b+w+4W7kgHoGdidOUejJd7FFa9510+9371FREJECUjIlKn+TKkd8E2bzIyrFMl74qseANcuRDfHTqOrHKMIlI9SkZEpM7Kd+ez9shaoOL+Ik63wdJdRwEYemZMJQ5+/Ld5RXRXRCSglIyISJ118hTwZ0SdUX7ZfcfIKXTTPDyocrOurnzbO9tqyy7Q6WI/RSwiVaFkRETqrOL+IpWZAn7Bdm8TzblntsRqreAuR2EOLH/Nu3zuJM22KhJg+g0UkTrLp/4i233oL7L6Pcg/Bs3aw1l6Bo1IoCkZEZE6yZcp4NOyCthyOAuLBQZ3aFH+gd2FsKzorsiQiWC1+SliEakqJSMiUif5MgX8wqK7It1aNaF5RHD5B974OeSkQmQCnHONX2IVkepRMiIiddLyw8uByk0BP78oGRla0URnhgFLX/Eu978D7EHVilFE/EPJiIjUOaZplkwBX1Ey4vYYLN6RAcDQThUM6d05F9K3QlAk9L7FH6GKiB8oGRGROmfX8V1k5GcQYguhe0z5U8BvOHiCE/kumoQ66N66/OYclrzsfe1zC4RUUFZEao2SERGpc1akeu+K9IzpSbCt/D4gxaNoBndsgb28p/SmrIF9i8Fqh+Q/+y1WEak+JSMiUucsP1TUXySh4v4iCyrbX6T4rsg5V0OTVtWKT0T8S8mIiNQpbsPNqrRVACTHJ5db9mhOIb8cPA7AsPKSkcw9sOVb7/LAu/0Rpoj4kZIREalTfs34lVxXLk2Cm9C5aedyyy7emYFpQpf4KGKiQk5fcNlrYBrQYQTEnuXniEWkupSMiEidUjyKpl9cP2wVTEi2ZKd3FM2QjuVMdJaXCev+5V0e+H9+iVFE/EvJiIjUKcWdV5Pjym+iMU2TJTu9T+kdVN6sq6vfA3c+xHWDtuf6LU4R8R8lIyJSZ+S781l/ZD1QcefVfUfzSDmej8NmoW9S07ILeVyw6l3vcv87oYKH7YlIYCgZEZE6Y13aOlyGi7jwONpEtim37JJd3iaaXm2aEhZkL7vQ5m8g+xCEx8DZ/8/f4YqInygZEZE64+Qp4C0V3MUo7i9SbhPNihne1z63gr2CZ9aISMAoGRGROqM4GaloSK9hmCzbVdxfpHnZhQ6ugYOrwOrwJiMiUmcpGRGROuF44XG2Zm4FKn4ezebDWRzLcxERbKdb6+iyC614w/t69lUQGevHSEXE35SMiEidsDptNSYmHaI70CK0nKYXfmuiSW7bDEdZU8BnHYZNX3mX+9/h71BFxM+UjIhInVAypLeCJhqAJUVNNANP119k9XtguCGxPyT09FuMIlIzlIyISJ2wMnUlUHETTaHbw6o9mQAMLisZcRV4kxHQXRGRekLJiIgE3HHjOAdyDmCz2OgT26fcsuv2Hyff5aFFRDBnxkacWuDXLyEvA6JaQ+dLayhiEfEnJSMiEnC7XLsAOKvFWUQElZFgnGRpUX+Rge2bnzr81zR/G87b7zawnWb+ERGpU5SMiEjA7XbvBiqeAh5+6y9SZhPNwVWQ+gvYQ6DXzX6NUURqjpIREQko0zTZ5fbeGamov0h2gYv1B44DMLCs+UVWveN9PfsqCGvmzzBFpAYpGRGRgNqTtYccM4dgWzDdY7qXW3blnkw8hskZzcNo3TSs9MbcjN+G8/b9Yw1FKyI1QcmIiARU8Sia7i26E2wrf8r2cp/Su+6f4HFCQi9o1dvvcYpIzVEyIiIBtSptFQD94vpVWLbkeTTtf5eMGB5YVTSct+9tfo1PRGqekhERCRiP4WF12moA+sWWn4xk5BSyLS0bgAHtf9dfZMdcOLEfQqL1dF6RekjJiIgEzNbMrWS7sgkmmM7NOpdbdmXRRGed4yJpFh5UemNxx9WeN4AjtCZCFZEapGRERAKm+Cm9be1tsVvLnxNk+W5vf5H+7X53VyRzN+z8ybusp/OK1EtKRkQkYFYc9j6Ppr2jfYVlf0tGfjdkd/V7gAkdRkDzio8jInWPkhERCQinx8m6I+sAaGdvV27ZjJxCtqflANCv7Ul3Rlz5sO5f3mV1XBWpt5SMiEhAbEjfQIGngOYhzYmxxpRb9rT9RTZ9BfnHoEkidBxVk+GKSA1SMiIiAVHcRNM3tu+pz5j5ndP2F1nzgfe1981gtfk7RBGpJUpGRCQgipORyswvUmYykrYZDqwAqx163lgjMYpI7VAyIiK1LteVy68ZvwKVm1+kuL9IctuTOq+ued/72ulCiIyrkThFpHZUKRl57bXXSEpKIiQkhOTkZFauXFlu+ePHj3PXXXcRHx9PcHAwZ555JrNmzapSwCJS/61JW4PbdNMqohUJEQnllj25v0jT4v4izjzYMNO73HtcTYYqIrWg/IH9ZZg5cyYTJ05kxowZJCcnM336dEaPHs22bduIiTm1E5rT6WTkyJHExMTwxRdf0KpVK/bt20d0dLQ/4heReqi4iaaip/TCaZpoNn0FhScg+gxoN7xGYhSR2uNzMjJt2jTGjx/PuHHev0ZmzJjB999/z3vvvcdDDz10Svn33nuPzMxMli5disPhACApKal6UYtIvVY82VlyfHKFZZftKiMZKW6i6X0zWNXaLFLf+ZSMOJ1O1qxZw+TJk0vWWa1WRowYwbJly8rc59tvv2XAgAHcddddfPPNN7Rs2ZKxY8fy4IMPYrOV3fu9sLCQwsLCkvdZWVkAuFwuXC6XLyHXacV1aUh18lVjvwaNsf6ZBZlsP7YdgF4tepV7DY7mFLLjiLe/SK/ESG+ZtE04Dq7CtNpxnz0G6vm1a4w/A7/X2K9BQ65/ZevkUzKSkZGBx+MhNja21PrY2Fi2bt1a5j67d+/m559/5vrrr2fWrFns3LmTO++8E5fLxZQpU8rcZ+rUqTz55JOnrJ8zZw5hYWG+hFwvzJ07N9AhBFxjvwaNqf4bnRsBiLPGsfzn5SXry7oG645aABsJYSbL5nunfD/nwEe0Aw5F9WT1wjW1EXKtaEw/A6fT2K9BQ6x/Xl5epcr53EzjK8MwiImJ4a233sJms9G7d29SUlJ4/vnnT5uMTJ48mYkTJ5a8z8rKIjExkVGjRhEVFVXTIdcal8vF3LlzGTlyZEkTVmPT2K9BY6z/mhVrYBec3/F8Lup9UbnXYOV3W4ADjOh2Bhdd1BmcudhfvguA2Asf5KJ2w2q/An7WGH8Gfq+xX4OGXP/ilo2K+JSMtGjRApvNRlpaWqn1aWlpxMWVPbQuPj4eh8NRqkmmS5cupKam4nQ6CQoKOmWf4OBggoODT1nvcDga3DcKGm69fNHYr0Fjqv/KNO/ou4GtB5aqc1nXYOXeY96yHVp6t/36XyjMhqZJ2Due36D6izSmn4HTaezXoCHWv7L18ek3OSgoiN69ezNv3rySdYZhMG/ePAYMGFDmPoMGDWLnzp0YhlGybvv27cTHx5eZiIhIw3Ug+wApOSnYLXb6xPYpt2zGSf1FSuYXWV3ccfWWBpWIiDR2Pv82T5w4kbfffpsPP/yQLVu28Oc//5nc3NyS0TU33XRTqQ6uf/7zn8nMzOSee+5h+/btfP/99zzzzDPcdddd/quFiNQLxUN6u7XsRpij/P5fK3b/bn6RtE2Qsto742qP62s8VhGpPT73GRkzZgzp6ek8/vjjpKam0qNHD2bPnl3SqXX//v1YT/qLJTExkR9//JH77ruPbt260apVK+655x4efPBB/9VCROqF4mSkMkN6V+z53ZDetR95XztdBBHlP1hPROqXKnVgnTBhAhMmTChz2/z5809ZN2DAAJYvX35qYRFpNAzT8CkZKZ55NbltM3AVwIZPvRt63VxjMYpIYKjRVURqxY5jOzhWeIxQeyjdWnQrt+yxXCdbU7MB6Ne2GWz9LxQch6jW0F4zroo0NEpGRKRWFM+62ju2Nw5b+T3sV+313hXpEBNB84hgWPuhd0PPG8Ba9mSJIlJ/KRkRkVpRnIxU5nk0xU00/do2g8zdsGchYPEmIyLS4CgZEZEa5/K4WJPmnS21UsnI3pP6i6z9p3dlh/MhOrHGYhSRwFEyIiI17peMX8h359M0uCkdm3Yst2xOoZtfU04A0LdNFKz/2Luh1001HaaIBIiSERGpcSePorFayv/YWbPvGIYJic1CSTiyCHLSIKwFnHlhbYQqIgGgZEREalxxf5FKzS+y2zu/SHLb5r/NLdJjLNg1Y7NIQ6VkRERqVK4rl43p3if1+jK/yNA4F+z40btSTTQiDZqSERGpUatTV+M23bSKaEViZPkdUAtcHjYcPA7A4Nw5YBrQZiC0KL+fiYjUb0pGRKRGLTu8DIABCWU/TPNk6/Yfx+UxiYt0EL1tpndlrxtrMjwRqQOUjIhIjVp2qCgZia84GSluorku7iCWY3shKBK6Xl6T4YlIHaBkRERqTGpuKrtP7MZqsVauv8heb+fVSz3zvCvOuQqCwmsyRBGpA5SMiEiNKb4rclbzs2gS3KTcsk63wZp9x4gkj6S0ud6VPdVEI9IYKBkRkRpT3F+kMrOubjqURYHL4NrQFVg9hdCyC7TqXdMhikgdoGRERGqEYRolk51VpvPqyr3HALg+aKF3Ra8bwWKpsfhEpO5QMiIiNWL7se1kFmQSag+lR8seFZZfte8YnS37SSrcBlYHdBtT80GKSJ2gZEREakRxf5G+cX1x2BzlljVMWLPvONfY5ntXdLoQwlvUbIAiUmcoGRGRGrH00FKgckN6D+WBszCf/2db7F2hjqsijYqSERHxuwJ3AWvT1gKV6y+yM8vCCOsaoi05EJkAHc6v6RBFpA5RMiIifrf2yFqchpOYsBjaNWlXYfndWRbG2OZ73/QYC1ZbjcYnInWLkhER8bvlh7xP6R0QPwBLBSNiTNMkNyuTIVbvw/ToeX1NhycidYySERHxO1+eR7MnI48LzEVYLSbGGYOhWcV3UkSkYVEyIiJ+lZGfwdbMrUDlJjtbtfdoySgaqx6KJ9IoKRkREb8qnuisU9NONA9tXmH5Y1vm08aaTqEtHLpcVtPhiUgdpGRERPyqeH6RgQkDK1W+Y8o3AGQkXQJBYTUWl4jUXUpGRMRvTNMsmV+kf0LFTTSH0tIY5vGWj+p/c43GJiJ1l5IREfGb7ce2k56fTqg9lN6xFT/k7siSfxFicbGb1oSc0bcWIhSRukjJiIj4zeIU7wyqfeP6EmwLrrB88x2fA7Ai9Fw9FE+kEVMyIiJ+s+TQEgAGtxpcceG0TSTmb8Fl2jjcvHL9S0SkYVIyIiJ+kevKZV3aOgAGJ1ScjOSv/BCAeUYv4qKjajQ2EanblIyIiF+sOLwCt+mmTWQbEqMSyy/sdmLb+BkAiyMuILz8h/qKSAOnZERE/GJJireJZlCrQRUX3v4DQc5jpJnR0GF4zQYmInWekhERqTbTNH3rL7LuXwD8xzOE3kktazI0EakHlIyISLXtydpDSk4KQdYg+sT2Kb9w1iHMnT8B8JlnGH2SmtZChCJSlykZEZFqK26i6R3bmzBHBbOorv8Yi2mwwuiMp2l74qJCaiFCEanLlIyISLVVur+IYZQ00XzmHka/ts1qOjQRqQeUjIhItRS4C1idthqoRH+RfUvg2F7yLKHMMvrRL0nJiIgoGRGRalqdtppCTyFx4XG0a9Ku/MLr/gnAd54B5BNCcjslIyKiZEREqql4CvjBrQZjKW9K9/zjsNn7hN5/u4YRGxVMm2Z6Sq+IKBkRkWoq7i9S4ayrv34J7gIywtqx3mxPv7bNy09eRKTRUDIiIlV2MPsge7P2YrfY6Rffr/zCRU00PzhGAhZ1XhWREkpGRKTKFh5cCED3mO5EBkWevmDqr3BoHabVweuZvQFIVjIiIkWUjIhIlRUnI8NaDyu/YNFw3uNtRnDYFUGz8CA6xkTUcHQiUl8oGRGRKsl15bIydSUA5yaee/qC7kL4ZSYASyMvAqBvUlP1FxGREkpGRKRKlh9ajstwkRiZSNuotqcvuPW/kJ8JkQl8eaIjAP3aNq+lKEWkPlAyIiJVsuDgAgCGth5a/l2OtR8BYPS4nlX7sgD1FxGR0pSMiIjPDNMo6S8yNHHo6Qse2wu75wMWdrS6guxCNxHBdrrER9VGmCJSTygZERGfbcrYxNGCo4Q7wukd0/v0BYs6rtJuGEsywgHok9QUm1X9RUTkN0pGRMRnxU00AxMG4rA5yi7kccO6j73LvW5ixZ6jACSrv4iI/I6SERHxWcmQ3sRhpy+0ax5kH4LQZpidLmLlnkwATXYmIqdQMiIiPknNTWVL5hYsWMp/Sm9Rx1W6X8fOTBfH8lyEOKyc06pJ7QQqIvWGkhER8UnxXZFuLbvRLOQ0dzmyU2HbD97lXjexouiuSK82TQmy62NHRErTp4KI+KRkFE3rckbRrP8ETA8kJkNMZzXRiEi5lIyISKXlu/NZfng5UM6QXtP8rYmm102YplnSeVXJiIiURcmIiFTaysMrKfQUEh8eT8fojmUX2rsYju2BoEjoegX7M/NIyyrEYbPQM7Fp7QYsIvWCkhERqbTiIb3ntj739LOurv3Q+3rOVRAcwfLd3rsiPRKjCQ2y1UaYIlLPVCkZee2110hKSiIkJITk5GRWrlxZqf0+/fRTLBYLV1xxRVVOKyIBZJgGCw78NgV8mfIyYfO33uVeNwGwfLe3v0j/dppfRETK5nMyMnPmTCZOnMiUKVNYu3Yt3bt3Z/To0Rw5cqTc/fbu3cukSZMYMmRIlYMVkcDZmLGRI/lHCHeEkxyfXHah9Z+ApxDiukFCL0zTLLkzomRERE7H52Rk2rRpjB8/nnHjxtG1a1dmzJhBWFgY77333mn38Xg8XH/99Tz55JO0a9euWgGLSGDM2zcPgHNbnUuQLejUAqYJaz7wLvcZBxYL+zPzOHyiAIfNQq826i8iImWz+1LY6XSyZs0aJk+eXLLOarUyYsQIli1bdtr9nnrqKWJiYvjjH//IokWLKjxPYWEhhYWFJe+zsrxP+nS5XLhcLl9CrtOK69KQ6uSrxn4N6kv9TdPkp30/ATCs9bAy47XsW4L96A5MRzjuzleAy8WSHd47pt1bN8FuMXC5jFP2qy/XoKY09vqDrkFDrn9l6+RTMpKRkYHH4yE2NrbU+tjYWLZu3VrmPosXL+bdd99l/fr1lT7P1KlTefLJJ09ZP2fOHMLCwnwJuV6YO3duoEMIuMZ+Dep6/dM8aRzIOYAdOzkbc5j166xTyvTe+zqtgX1Rfdkwz/tHx392WAErzdyZzJp16j4nq+vXoKY19vqDrkFDrH9eXl6lyvmUjPgqOzubG2+8kbfffpsWLVpUer/JkyczceLEkvdZWVkkJiYyatQooqIazqPHXS4Xc+fOZeTIkTgcp3nYWAPX2K9Bfan/Wxvfgo0wsNVArhx65akF8o5if/k2AFpd/iit4ntgmiZTNy0ECrl+ZF8Gti+7z0h9uQY1pbHXH3QNGnL9i1s2KuJTMtKiRQtsNhtpaWml1qelpREXF3dK+V27drF3714uvfTSknWG4b1Na7fb2bZtG+3btz9lv+DgYIKDg09Z73A4Gtw3ChpuvXzR2K9BXa///JT5AIw4Y0TZcW76HDxOiO+Bo01fAPYdzSW1aH6Rfu1a4nCUP6y3rl+DmtbY6w+6Bg2x/pWtj08dWIOCgujduzfz5s0rWWcYBvPmzWPAgAGnlO/cuTMbN25k/fr1JV+XXXYZw4cPZ/369SQmJvpyehEJgIPZB9mauRWbxVb2U3pP7rja+5aS1cWjaHomNtX8IiJSLp+baSZOnMjNN99Mnz596NevH9OnTyc3N5dx48YBcNNNN9GqVSumTp1KSEgIZ599dqn9o6OjAU5ZLyJ107z93j8+esf2pmlIGSNi9i6GozshKALO+UPJ6t/mF9EU8CJSPp+TkTFjxpCens7jjz9OamoqPXr0YPbs2SWdWvfv34/VqoldRRqK4mTk/Dbnl11gzfve13OuhuBIAM0vIiI+qVIH1gkTJjBhwoQyt82fP7/cfT/44IOqnFJEAiAjP4P1R9YDcF6b804tkJsBW77zLp/URFM8v0iQzUpPzS8iIhXQLQwROa2f9/+Mick5Lc4hLvzUTuqs+6e342pCT0joUbJaz6MREV8oGRGR0/p5/8/Aae6KGB5YXTTzct/bSm1SfxER8YWSEREpU5YzixWHVwAwos2IUwvs/AmO74eQaDjr/5WsVn8REfGVkhERKdOCAwtwm27aN2lPUpOkUwusesf72vMGCPptZmT1FxERXykZEZEyzd47G4CRSSNP3Zi5B3YUTV3d59ZSm9RfRER8pWRERE5xovAES1OWAnBh0oWnFlj9HmBC+/OheelZlJftKm6iUX8REakcJSMicoqf9v2E23TTqWkn2kW3K73Rle8dRQPQb3ypTaZpsqQ4GTnNs2hERH5PyYiInOKHvT8AcEHbC07duOkryD8GTRKh46hSm3YeySE9u5AQh5Ve6i8iIpWkZERESsnIz2BV6ioALkgqIxkp7rjaZxxYS/cJWbIzA4C+Sc0IqeDBeCIixZSMiEgpc/bOwTANurXoRuvI1qU3pqyFlDVgC4KeN52y7+Kd3iaage1b1EaoItJAKBkRkVKKR9GU2USz6l3va9crIKJlqU1uj8GKopE0gzsoGRGRylMyIiIlDuccZt2RdViwMOqM0v1ByD0Kv37hXf7djKsAG1NOkF3opkmog64JUbUQrYg0FEpGRKTEj3t/BKB3bG9iw2NLb1zzPrgLIL4HJPY7Zd/i/iID2jXHZrXUdKgi0oAoGRGREsWjaC5s+7u5RTyu35po+v8ZLKcmG0uK+osM6qgmGhHxjZIREQFgX9Y+Nh/djM1iY8QZv3sWzeZvIPsQhMfAWVeesm++08OafccAGKT5RUTER0pGRASA2Xu8HVf7x/enWcjvZk9dMcP72vePYA8+Zd/V+zJxegzim4TQtkV4TYcqIg2MkhERwTRNfthzmonODq6Bg6u8w3l/9xyaYiVNNB1aYCmjCUdEpDxKRkSEzZmb2XViF0HWIM5rc17pjSve8L6efRVExJS5f3Hn1UEd1EQjIr5TMiIifLvzWwDOb3M+UUEnDcvNOuyd/h0g+Y4y9z2e5+TXQycATXYmIlWjZESkkXN6nHy/53sALutwWemNq98Fww1tBkBCjzL3X777KKYJHWMiiI0KqeFoRaQhUjIi0sgtPLiQE4UniAmNYUD8gN82uApg9fve5eQ/nXb/xSVNNLorIiJVo2REpJH7Ztc3AFzS/hJsJz/4buPnkJcBUa2h86Wn3X/pSZ1XRUSqQsmISCOWkZ/BooOLALi8/eW/bTAMWPqKdzn5drDZy9z/8Il8dmfkYrVAcrtmZZYREamIkhGRRmzW7ll4TA/dWnSjXXS73zbsmAMZ2yAoEnrfctr9F233NtF0T4wmKsRRw9GKSEOlZESkEStuorms/e86ri592fva5xYIaXLa/edvPwLA0DNbnraMiEhFlIyINFJbM7ey/dh2HFZH6YnODq6BfUvAaofkP592f7fHYNEO750RJSMiUh1KRkQaqW92eu+KnNfmPJoEn3T3Y+lL3tdzroYmrU67//oDx8kucBMd5qBb6+gajFREGjolIyKNkMvj4vvd3rlFSnVczdwNW77zLg+8u9xjLNieDsCQji2xWTUFvIhUnZIRkUZoYcpCjhUeo0VoCwYknDS3yLLXwTSgwwiIPavcY8zf5k1GhqmJRkSqScmISCP0+fbPAbi0/aXYrUXDdnOPwrp/eZcH/l+5+2fkFLIxxTsF/JAzNb+IiFSPkhGRRuZA9gGWpiwF4OqOV/+2YdU74M6H+O7Q9txyj7Foh/euyFkJUcREagp4EakeJSMijczn2z/HxGRgwkASoxK9K525sPJN7/LA/wNL+X1AFhQ10WgUjYj4g5IRkUbE6XHy9Y6vAbim0zW/bVjzAeQdhaZtoesV5R7DMEwWakiviPiRkhGRRmTOvjkcKzxGbFgsQ1sP9a50FcCSoknOhkw87dTvxTamnCAz10lksJ1eZzSt4YhFpDFQMiLSiHy27TMArjrzqt86rq7/F+Skeh+I1+3aCo9RPKR3UIcWOGz6CBGR6tMniUgjsf3YdtYdWYfNYuOqjld5V7qdsHi6d3nwvWAPqvA4xcnI0E5qohER/1AyItJIFN8VOa/NecSExXhX/jITThyAiFjoeWOFxzie52Td/mMAnKv+IiLiJ0pGRBqBXFcu3+3yzqxa0nHV44bF07zLA/8PHBUP0V28MwPDhI4xEbSKDq2pcEWkkVEyItIIfL/7e/LceSRFJZEcl+xduekr7/Tvoc2gz7hKHUdDekWkJigZEWngTNNk5raZAFx95tVYLBYwDFj0grfAgLsgKLzC4xiGyf+Kp4DvFFNj8YpI46NkRKSBW5W6iu3HthNiC+HyDkUPxdvyLaRvhZAm0O/2Sh1n3YHjZOQUEhlsp1/bZjUYsYg0NkpGRBq4DzZ9AMDlHS6nSXATMDzwv2e8G5PvgJCoSh1n7uY0wDuKJsiujw4R8R99oog0YLuO72JRyiIsWLip603elRs/h4xtEBLtbaKppLmbUwEY2TW2BiIVkcZMyYhIA/bR5o8AOL/N+bSJagMeF8yf6t046B5vM00l7E7PYVd6Lg6bheGd1V9ERPxLyYhIA5WRn1EynPfms272rlz3Tzi2F8JjIPlPlT5WcRNN/3bNiQpx+DtUEWnklIyINFCfbPkEl+Gie8vu9Ijp4X0GzYLnvRuH/KVSI2iKFScjaqIRkZqgZESkAcpz5ZUM573lrFu8K1e/C9mHvM+gqeS8IgAZOYWsKZp1dUQXJSMi4n9KRkQaoK93fk2WM4vEyESGJw6HwmxY9A/vxqEPgD240sf6ecsRTBPObhVFgmZdFZEaoGREpIHxGJ6Sjqs3db0Jm9UGy2dA3lFo1g56jPXpeHOKm2i6xPk9VhERUDIi0uD8tP8nUnJSiA6O9k5ylnsUlr7i3TjsYbBVvgNqvtPD4p3eWVfVX0REaoqSEZEGxDAN3v7lbQDGdBpDqD0UFjwLhScg9hw4+yqfjrdoRzoFLoNW0aF0iY+siZBFRJSMiDQk/9v/P7Yd20a4I5wbutwAGTu8HVcBRv8VrL79yp88isZisfg7XBERAOyBDkBE/MMwDV7f8DoAYzuPJTokGr76MxhuOPMCaDfMp+N5DJOftx4BYJSaaESkBunOiEgDMW//PLYf2064I9w7ydmehbBtFlhsMPJpn4+3dv8xjuY6iQqx01cPxhORGqRkRKQBMEyDNza8AcD1Xa6niSMSfnzEu7HPrdDyTJ+P+f0vhwE4v0ssDps+KkSk5ugTRqQB+GnfT+w4toMIR4T3gXi/fAqpv0BwExj2kM/H8xgm32/0JiOXdo/3d7giIqVUKRl57bXXSEpKIiQkhOTkZFauXHnasm+//TZDhgyhadOmNG3alBEjRpRbXkR8c8pdEYsd5j3l3XjuJAhv4fMxV+w5Snp2IdFhDgZ3aOnPcEVETuFzMjJz5kwmTpzIlClTWLt2Ld27d2f06NEcOXKkzPLz58/nuuuu43//+x/Lli0jMTGRUaNGkZKSUu3gRQTm7pvLzuM7iXREcmPXG2HJS5B9GKLP8OlheCf7bsMhAC48O44gu26gikjN8vlTZtq0aYwfP55x48bRtWtXZsyYQVhYGO+9916Z5T/++GPuvPNOevToQefOnXnnnXcwDIN58+ZVO3iRxs4wDWZsmAHADV1voElOBiye7t048imfpn0v5nQb/PBrKgCXdkvwV6giIqfl09Bep9PJmjVrmDx5csk6q9XKiBEjWLZsWaWOkZeXh8vlolmz0/fOLywspLCwsOR9VlYWAC6XC5fL5UvIdVpxXRpSnXzV2K9Bdev/7e5v2Xl8JxGOCK7tMAbjP7dh9RRitBuOp+NFUIXjLtiezvE8Fy0iguiVGFXj3xv9DDTu+oOuQUOuf2XrZDFN06zsQQ8dOkSrVq1YunQpAwYMKFn/wAMPsGDBAlasWFHhMe68805+/PFHNm3aREhISJllnnjiCZ588slT1n/yySeEhYVVNlyRBs1pOnkx60WyzWxGh4zmmoIQ+u15BY/Fzv86P0NuSNWeJfOvHVZWZVg5N87gqraGn6MWkcYkLy+PsWPHcuLECaKiok5brlYnPfv73//Op59+yvz580+biABMnjyZiRMnlrzPysoq6WtSXmXqG5fLxdy5cxk5ciQOR+WfF9KQNPZrUJ36v7nxTbI3ZpMQnsATI/9C+DvDvRsG3cvQobdWKZ4Cl4eH184HPNx1aX96tYmu0nF8oZ+Bxl1/0DVoyPUvbtmoiE/JSIsWLbDZbKSlpZVan5aWRlxc+X+FvfDCC/z973/np59+olu3buWWDQ4OJjj41LZuh8PR4L5R0HDr5YvGfg18rf+RvCN8tMX7ZN77+txHxIrXvJ1WmyZhGzoJWxWv5bxtGeQWemgVHUrfti2wWmtvCnj9DDTu+oOuQUOsf2Xr41MH1qCgIHr37l2q82lxZ9STm21+77nnnuPpp59m9uzZ9OnTx5dTikgZXln3CvnufLq37M7okERY5p0GnoteAEdolY/73Qbv3CKXdI+v1URERBo3n5tpJk6cyM0330yfPn3o168f06dPJzc3l3HjxgFw00030apVK6ZOnQrAs88+y+OPP84nn3xCUlISqaneXvoRERFERET4sSoijcPWzK18s/MbAO7vPQnL938B0wNdLoWOI6t83JxCN/O2eu96ahSNiNQmn5ORMWPGkJ6ezuOPP05qaio9evRg9uzZxMZ6H6S1f/9+rCc9GfSNN97A6XTyhz/8odRxpkyZwhNPPFG96EUaGdM0eWHVC5iYXJh0Id33r4b9y8ARBhf8vVrHnrcljQKXQbsW4ZyV0HD6ZolI3VelDqwTJkxgwoQJZW6bP39+qfd79+6tyilEpAwLDy5kReoKgqxB3NPhKvjgSu+G86dAk9bVOva3670TnV3SPQGLRU00IlJ7NLWiSD1R4C7g2VXPAnBDl+tpNfdpcOVCm4HQ7/ZqHTs9u5AF29MBuEzPohGRWqZkRKSeePOXNzmQfYCYsBjGu4Nh7yKwh8Llr4K1er/KX649iNsw6dkmmg4xkX6KWESkcpSMiNQD249t54NfPwDg4bPGEzHvb94NI6ZA8/bVOrZpmsxcdQCAa/smVutYIiJVoWREpI4zTIOnlj2F23RzXuJwzl/18UnNM1V7EN7JVuzJZE9GLuFBNi7RKBoRCQAlIyJ13Bfbv2BD+gbCHeFMDmkLexb6rXkGKLkrclmPBMKDa3VSZhERQMmISJ2WnpfO9DXTAbi7wzXE/Vw0fNcPzTMAJ/JczNronehsTN821T6eiEhVKBkRqcP+vvLvZLuyObtZV65dNRPcBdD+fL80zwB8vT6FQrdB57hIurdu4pdjioj4SsmISB31076fmLNvDjaLjSnuCGzpWyE8Bq6c4ZfmGdM0+ffK/YC346rmFhGRQFEyIlIHHck7whPLngDglthBdN7whXfD/3sTImL8co5fDp5ga2o2QXYrV/Rs5ZdjiohUhZIRkTrGMA0eXfwoJwpP0KVJe+5a9513w+D7oP15fjvPp0UdVy86O47osCC/HVdExFdKRkTqmI+3fMyyw8sIsYXw96NZOApOQOu+MPwRv50jt9DNt+tTAHVcFZHAUzIiUodsP7a9ZPTMpNB2tDuwBoKbwFXvgs3ht/N8t+EQuU4PSc3D6N+umd+OKyJSFUpGROqIQk8hDy16CKfhZGhke67ZONu74co3oOkZfjuPYZi8s3gPAGOT26jjqogEnJIRkTpi+prp7Di2g2aOKJ7csgwLwLCHofPFfj3P/O1H2Hkkh4hgO9f2UxONiASekhGROmD23tn8a8u/AHg64yjNXQXQ+RI4936/n+vNBbsBuK5fIlEh/mv6ERGpKs39LBJghz2HeXfFuwCM94RxbuZWiOnqt/lETrbhwHFW7MnEbrUwblBbvx5bRKSqdGdEJIBOFJ7gk9xPKPAUMMgWzV37t0JINFz7MQRH+v18by3y3hW5rHsCCdGhfj++iEhVKBkRCRCP4WHykskcM47R2hbOs7t/xWaxwdXvQ7N2fj/f/qN5/FD0HJrbhvj/+CIiVaVmGpEAeWXdKyxPXU6waWX6vp00MQy47FW/Tmx2sveW7MEwYUjHFnRNiKqRc4iIVIXujIgEwHe7vuPdX739RJ5KP0InlwvOexR63Vgj5zuW62Rm0Yyrfzq3+k/7FRHxJyUjIrVsScoSHl/yOADjsnK4KDcPT+9bYcikGjvnxyv2ke/y0DU+ikEdmtfYeUREqkLJiEgt2pSxifvm34fbdHNRnpN7j2ZyqEkfjFFToYYmH8tzuvlg6V4Abj+3nSY5E5E6R8mISC3Zl7WPO+fdSb47n/6Fbv6algqJ/VmTdAdYbTV23veX7CUjx0lis1Au7hZfY+cREakqJSMitSAjP4M/zf0TmQWZdHF5mH74MI7W/fCM+TeGteaemJuZ62TG/F0ATBrVCYdNv/IiUvdoNI1IDTtWcIw/zf0TKTkpJLo9vH7oMOGt+8H1X4CtZuf6ePXnnWQXuukaH8Wl3RJq9FwiIlWlP5NEatDR/KPc+uOtbD+2neYegzcPp9GiVV+44UsIqdnhtQcy8/jn8r0APHRhZ6xW9RURkbpJyYhIDUnPS+fWH29l5/GdxHgM3j+cSmJ8b28iUgOzq/7etLnbcXlMBndowblntqzx84mIVJWaaURqQGpuKrfNuY19WfuIdXt473AabVr1h7Gf1koisunQCb5enwLAgxd0rvHziYhUh5IRET9LyUnhth9v42DOQRJcbt5NTaP1mZfClW+CI6RWYnhu9jZMEy7tnsA5rZvUyjlFRKpKzTQifrQxfSNjvx/LwZyDtHa5eD81jda9b4c/vF9ricjSnRks2J6Ow2Zh0qgza+WcIiLVoTsjIn4yb988Hlr0IAWeQjoVOnktLZ3Y85+EARNqbEKz3ytweXjsm18BGNuvDWc0D6+V84qIVIeSEZFqMk2TjzZ/xD9W/wMTkyF5+TyfmUP4FW/BOX+o1Vhe+XkHu9JzaRkZzMSRnWr13CIiVaVkRKQanB4nz658ls+2fwbAmKxsHnJHYB/3BST0qNVYfk05wYwFuwF4+vKzaRLmqNXzi4hUlZIRkSpKyUlh0vy/8OvRTVhMk79kHuem5j2x/OEDCK/dh9G5PAYPfPELHsPk4nPiueDsuFo9v4hIdSgZEamC/+3/H48smky2O5coj4ep6Uc5t+ftcP4UsNX+r9WbC3ax+XAW0WEOnrjsrFo/v4hIdSgZEfGBy3DxytqXeX/TBwCcU1DIC1kuEi59G7peFpCYdqRl8/K8nQBMubQrLSODAxKHiEhVKRkRqaRtmdt4bNFkthzfAcANJ7KY2KQHjutmQFRgnobr9hg88OUvOD0G53WO4YoerQISh4hIdSgZEamAy3Dx7i/v8OaGGbgxiPJ4eCIzm5GDH4F+t4M1cNP1/P2Hrazbf5yIYDt/u/JsLLU0hFhExJ+UjIiUY1vmNh6d/xe2Zu8DYHhuHo/ZW9Pyxi8gtmtAY/tq3UHeWbwHgOf/0I34JjX7BGARkZqiZESkDCcKT/D66heZufM/eDBp4vHw8Il8LhzwEJZ+t4HVFtD4Nh48wUNfbgRgwvAOXHhOYJqJRET8QcmIyEk8hocvt87klTUvctwoAGBkbh4PN0+mxR/+EbC+ISfLyCnkT/9cTaHb20/kvpGa8l1E6jclIyJ4Z1FddmgZ05ZMYVt+KgAdnE4ecEcwYOQ06DgywBF6uTwGd368lkMnCmjXIpwXx/TAZlU/ERGp35SMSKO36tAKXl32NGtzvP1CIj0Gd+V5GNP/Qew9bwrIvCFlMQyTh/+zkZV7MokItvPWTb1pEqpZVkWk/qsbn7IiAbDm8EpeX/o0K3P2AhBkmFydW8CfutxA08GTIDgisAGexGOYPPTlL3y+5iBWC7w4pgcdYiIDHZaIiF8oGZFGxW24mbfzOz5a9xq/FKQBYDdNrspzMr7D1cQO/guENQtwlKV5DJP7v9jAf9amYLNaeHFMD0Z2jQ10WCIifqNkRBqFbGc2X617k4+3z+RQUcdUh2lyWb6bP3W6lviB90FIkwBHeSq3x2DS5xv4ev0hbFYLL1/bk4u7Bb4TrYiIPykZkQbLNE3WHlzCf9a9xpzMTRRYTACaejyM8YQw5uxbaNH7jxAUHuBIy1bo9jDp81/4bsMh7FYLr1zXU0N4RaRBUjIiDc6hrAP8sP5Nvt43h71GvnelBdo7XdwQlsQlA/9CSIcRUIdnK005ns+dH69lw4HjOGwWXh3bi9Fn6Um8ItIwKRmRBiEt+xBz1r/J7P3z+MV9omR9qGFwodvO/zvjArr1m4AlOjGAUVbOwu3p3PPpOo7luYgKsfPydT0Z1ikm0GGJiNQYJSNSL5mmyfbUNSzc9C8WpK7kF3cWZtGdDotp0sfp4ZKmZ3FBn/8jLGlInb4LUswwTF75eSfT523HNOHsVlG8cX1vEpuFBTo0EZEapWRE6o3jeRms2voFy/f+xMKsnaRaPL9ttFjo6fQwuklnRp19Ay07XQq2+jMHx9bUbJ6etY2VezIBuK5fG6Zc2pUQR2CnnRcRqQ1KRqTOysxJZcP2b1m9/3+sPLGDbWZByd0PLBBiGPQ37Axpdjbndr6auDMvqTMTlFXW8TwXX+yxsmT5MgwTQhxW/nbFOVzVu3WgQxMRqTX165NbGqxCdz7b9//Mpv3z2XBkPevzD7P/5DsfABYLHVwe+ga3ZHCrwfTrdhMhLToFJuBqcroNPl9zgBd+3MaxPCsAF58Tz+SLOtO6qZplRKRxUTIitco0TY5mHWDXvgXsTFvDlqNb+TXnEE/MNHCf3K+jaLG926CHozn943rT58wradFmUMCfmFsdmblO/r1yPx8t20taViEAcaEmz13bh3M7abSMiDROSkakRrjchaSkrmXf4dXszdjMvuz97MlPZ6eRx/HfP9jNAWAh2mPQxRJMt/BEeiQkc06HS2gSe0696HxaHtM02XQoi49X7Oc/aw9S6DYAiIkM5vYhSTTL3MSAds0DHKWISOAoGZEqyS84QWr6RtKObiP12G4OZx8gJfcwKc7jpBgFpFlMjLKSCKsFi2mS6DFpbw+nY1gCIdlRjB56M4lnDMFiD6r9ytQAwzBZf/A4s39NZfavqezPzCvZdlZCFH8c3JZLuiVgMT3MmrUpgJGKiARelZKR1157jeeff57U1FS6d+/OK6+8Qr9+/U5b/vPPP+exxx5j7969dOzYkWeffZaLLrqoykFLzSgoOMHxE/s4dmIfmVkHyMw5TGbeEY7mZ5BeeJx0Vw4ZRgHpeMgq77H1VgALoYbBGaaNM+yRnBEWR1J0W9rH9aFtm3MJjUoAwOVyMWvWLOLbnIvFXn9Gv/yexzDZnpbN6n3HWL03k+W7j5Y0w4C3Y+p5nWO4eUAS/do2w1KUqLlcntMdUkSk0fA5GZk5cyYTJ05kxowZJCcnM336dEaPHs22bduIiTl1YqalS5dy3XXXMXXqVC655BI++eQTrrjiCtauXcvZZ5/tl0oIuJx55OWlk5d/lNy8o+QVHCOnIJPcgmPkFBwnpzCLHFc22c5ssty5ZLvzyTacnDCcHDc9ZFmgoLwEo1hRogHeCcXiTCtx1hDigiJpFRpHq6g2tG7emVax3WjR8px6nWCUxTRNMnOd7DySw44jOew8ksP2tGw2HjxBdqG7VNmIYDvndY7hwrPjGNqpJWFBuhEpIlIWnz8dp02bxvjx4xk3bhwAM2bM4Pvvv+e9997joYceOqX8Sy+9xAUXXMD9998PwNNPP83cuXN59dVXmTFjRjXDr12mYeDxODEMF25PIR53IR6P07vsceJ2F5S8d3ucuN2FuNwFRe+961yeQlzuQpzuAgpdBew9uptP5/6A23Dh9DhxGk5cHieFhotCj5NCw02h4aLAdFFoeigwPBTiId80yMekwAL5Fkp3/vTFSckFeJ9g29SAZthoag2iqT2U5kFRtAxpQcuIOJpHJtKySRKxLc8iskkbLFarX65toBiGSa7TTW6hh5xCNzmFbo7lOjmW5ySz6DUtq5DDJ/I5fKKAw8cLyD/N3YzwIBs92zSlT1JT+pzRjD5JTTVPiIhIJfiUjDidTtasWcPkyZNL1lmtVkaMGMGyZcvK3GfZsmVMnDix1LrRo0fz9ddfn/Y8hYWFFBb+dos7KysL8N7Sd7lcvoRcrjs/HMJeSw4G4LGYmIBR9OWxgIHF+94CHii7D0R12YD0bZUvX+r//lPjCTJNQg2TUNNS9GUjBDvBOAgiiGBCcVjCcFgjsFqisFmbYLG1AHsspj0Gj63FKaNVck3INWBvFpAFpABkA6fv62CWudI8pYxhGBzYb2X5N5uwWq2YmCXFzJN2M03v98c0wSheNkyMoveGaeI2TAyj6NU0cXtMnB4Dt+FddnkMClwGhW4PhW6DApeHfJdx2jqUp3XTUDq0DKdDTATtW4bTJS6STrER2G0nf4MMXBUcv/jn2Z8/1/VNY78Gjb3+oGvQkOtf2Tr5lIxkZGTg8XiIjY0ttT42NpatW7eWuU9qamqZ5VNTU097nqlTp/Lkk0+esn7OnDmEhflvDoajnjxSQ4r/Q69eomE3TWwm2DCxmxQtF72alqJlCzbTgrXoy2ZasJhWrKa16NUGpg2LaQfDDqYd07RjGg48ZjCGEYTHDMZtBOM0QnEZ4RQaoRQY4RQY4eQbUWQTXI1aFFKUadQyK6QF4rwnR2ASbIMQG4Q7INxuEm73Lkc5TKKDoWkQRAd5lx3WbCDbm6Wmwr5U2FeN88+dO9dPNam/Gvs1aOz1B12Dhlj/vLy8igtRR0fTTJ48udTdlKysLBITExk1ahRRUVF+O0/anCySs4+CxQ5Yi14tWCx2TOxYLDZMix0LdkyLAywObxmLHSzBmJYgsDiwWKt2GT2GwZ49e2jbti22et7cAVQqn7P8rpBpeNi9ew/t2rXFZvPekbFYispZfjuk1WIpWg+WomWb1VKy3mqxYLNasFks2Kze9w6bFYfN+2oveg2xWwm22wh2WAm2WwkPshEebCfYbi3pVFqbXC4Xc+fOZeTIkTgcDat/TWU19mvQ2OsPugYNuf7FLRsV8el/0RYtWmCz2UhLSyu1Pi0tjbi4sidsiouL86k8QHBwMMHBp/6F73A4/PqNuv3iG/12rKrwjiTZxUWjOzW4H8DKKrkGoxrvNQD//2zXR439GjT2+oOuQUOsf2Xr49Of40FBQfTu3Zt58+aVrDMMg3nz5jFgwIAy9xkwYECp8uC9FXW68iIiItK4+Ny+MHHiRG6++Wb69OlDv379mD59Orm5uSWja2666SZatWrF1KlTAbjnnnsYOnQo//jHP7j44ov59NNPWb16NW+99ZZ/ayIiIiL1ks/JyJgxY0hPT+fxxx8nNTWVHj16MHv27JJOqvv378d6Uv+HgQMH8sknn/Doo4/y8MMP07FjR77++mvNMSIiIiJAFTuwTpgwgQkTJpS5bf78+aesu/rqq7n66qurcioRERFp4BrAEA4RERGpz5SMiIiISEApGREREZGAUjIiIiIiAaVkRERERAJKyYiIiIgElJIRERERCSglIyIiIhJQSkZEREQkoKo0A2ttM00TqPyjiOsLl8tFXl4eWVlZDe5JjZXV2K9BY68/6Bo09vqDrkFDrn/x/9vF/4+fTr1IRrKzswFITEwMcCQiIiLiq+zsbJo0aXLa7RazonSlDjAMg0OHDhEZGYnFYgl0OH6TlZVFYmIiBw4cICoqKtDhBERjvwaNvf6ga9DY6w+6Bg25/qZpkp2dTUJCQqmH6P5evbgzYrVaad26daDDqDFRUVEN7gfQV439GjT2+oOuQWOvP+gaNNT6l3dHpJg6sIqIiEhAKRkRERGRgFIyEkDBwcFMmTKF4ODgQIcSMI39GjT2+oOuQWOvP+gaNPb6Qz3pwCoiIiINl+6MiIiISEApGREREZGAUjIiIiIiAaVkRERERAJKyUgd8/3335OcnExoaChNmzbliiuuCHRIta6wsJAePXpgsVhYv359oMOpNXv37uWPf/wjbdu2JTQ0lPbt2zNlyhScTmegQ6sxr732GklJSYSEhJCcnMzKlSsDHVKtmTp1Kn379iUyMpKYmBiuuOIKtm3bFuiwAubvf/87FouFe++9N9Ch1KqUlBRuuOEGmjdvTmhoKOeccw6rV68OdFi1TslIHfLll19y4403Mm7cODZs2MCSJUsYO3ZsoMOqdQ888AAJCQmBDqPWbd26FcMwePPNN9m0aRMvvvgiM2bM4OGHHw50aDVi5syZTJw4kSlTprB27Vq6d+/O6NGjOXLkSKBDqxULFizgrrvuYvny5cydOxeXy8WoUaPIzc0NdGi1btWqVbz55pt069Yt0KHUqmPHjjFo0CAcDgc//PADmzdv5h//+AdNmzYNdGi1z5Q6weVyma1atTLfeeedQIcSULNmzTI7d+5sbtq0yQTMdevWBTqkgHruuefMtm3bBjqMGtGvXz/zrrvuKnnv8XjMhIQEc+rUqQGMKnCOHDliAuaCBQsCHUqtys7ONjt27GjOnTvXHDp0qHnPPfcEOqRa8+CDD5qDBw8OdBh1gu6M1BFr164lJSUFq9VKz549iY+P58ILL+TXX38NdGi1Ji0tjfHjx/PPf/6TsLCwQIdTJ5w4cYJmzZoFOgy/czqdrFmzhhEjRpSss1qtjBgxgmXLlgUwssA5ceIEQIP8fpfnrrvu4uKLLy71s9BYfPvtt/Tp04err76amJgYevbsydtvvx3osAJCyUgdsXv3bgCeeOIJHn30Uf773//StGlThg0bRmZmZoCjq3mmaXLLLbdwxx130KdPn0CHUyfs3LmTV155hT/96U+BDsXvMjIy8Hg8xMbGllofGxtLampqgKIKHMMwuPfeexk0aBBnn312oMOpNZ9++ilr165l6tSpgQ4lIHbv3s0bb7xBx44d+fHHH/nzn//M//3f//Hhhx8GOrRap2Skhj300ENYLJZyv4r7CgA88sgjXHXVVfTu3Zv3338fi8XC559/HuBaVF1l6//KK6+QnZ3N5MmTAx2y31X2GpwsJSWFCy64gKuvvprx48cHKHKpLXfddRe//vorn376aaBDqTUHDhzgnnvu4eOPPyYkJCTQ4QSEYRj06tWLZ555hp49e3L77bczfvx4ZsyYEejQap090AE0dH/5y1+45ZZbyi3Trl07Dh8+DEDXrl1L1gcHB9OuXTv2799fkyHWqMrW/+eff2bZsmWnPJuhT58+XH/99fX6L4XKXoNihw4dYvjw4QwcOJC33nqrhqMLjBYtWmCz2UhLSyu1Pi0tjbi4uABFFRgTJkzgv//9LwsXLqR169aBDqfWrFmzhiNHjtCrV6+SdR6Ph4ULF/Lqq69SWFiIzWYLYIQ1Lz4+vtRnPkCXLl348ssvAxRR4CgZqWEtW7akZcuWFZbr3bs3wcHBbNu2jcGDBwPgcrnYu3cvZ5xxRk2HWWMqW/+XX36Zv/71ryXvDx06xOjRo5k5cybJyck1GWKNq+w1AO8dkeHDh5fcGbNaG+bNy6CgIHr37s28efNKhq8bhsG8efOYMGFCYIOrJaZpcvfdd/PVV18xf/582rZtG+iQatX555/Pxo0bS60bN24cnTt35sEHH2zwiQjAoEGDThnOvX379nr9mV9VSkbqiKioKO644w6mTJlCYmIiZ5xxBs8//zwAV199dYCjq3lt2rQp9T4iIgKA9u3bN5q/FlNSUhg2bBhnnHEGL7zwAunp6SXbGuLdgokTJ3LzzTfTp08f+vXrx/Tp08nNzWXcuHGBDq1W3HXXXXzyySd88803REZGlvSVadKkCaGhoQGOruZFRkae0j8mPDyc5s2bN5p+M/fddx8DBw7kmWee4ZprrmHlypW89dZbDfaOaHmUjNQhzz//PHa7nRtvvJH8/HySk5P5+eefG+eY80Zo7ty57Ny5k507d56SgJkN8OHaY8aMIT09nccff5zU1FR69OjB7NmzT+nU2lC98cYbAAwbNqzU+vfff7/CZj1pGPr27ctXX33F5MmTeeqpp2jbti3Tp0/n+uuvD3Rotc5iNsRPOREREak3GmaDtIiIiNQbSkZEREQkoJSMiIiISEApGREREZGAUjIiIiIiAaVkRERERAJKyYiIiIgElJIRERERCSglIyIiIhJQSkZEREQkoJSMiIiISEApGREREZGA+v/zeaHukOp4bgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = np.linspace(-7, 7, 100)\n",
    "for name, tfm in {\"probit\": iprobit, \"logit\": ilogit, \"cloglog\": icloglog}.items():\n",
    "    pp = tfm(f)\n",
    "    plt.plot(f, pp, label=name)\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "23",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(w_0, w_t, w_x, w_tx, w_p, xp, xt, t, p):\n",
    "    f = prognostic(w_0, w_x, w_p, xp, p) + t * ite(w_tx, w_t, xt)\n",
    "    pf = TFM_FUNCTION(f)\n",
    "    return pf\n",
    "\n",
    "\n",
    "def prognostic(w_0, w_x, w_p, x, p):\n",
    "    mu = w_0 + w_p * p + x @ w_x\n",
    "    return mu\n",
    "\n",
    "\n",
    "def ite(w_tx, w_t, x):\n",
    "    tau = x @ w_tx + w_t\n",
    "    return tau\n",
    "\n",
    "\n",
    "def model_treatment_intersection(xp, xt, t, p, y):\n",
    "    n, d = xp.shape\n",
    "    assert(d == xt.shape[1])\n",
    "\n",
    "    # Hyper Priors\n",
    "    l_0 = pyro.sample(\"l_0\", dist.Uniform(0, 100))\n",
    "    l_x = pyro.sample(\"l_x\", dist.Uniform(0, 100))\n",
    "    l_p = pyro.sample(\"l_p\", dist.Uniform(0, 100))\n",
    "    l_t = pyro.sample(\"l_t\", dist.Uniform(0, 1000))\n",
    "    l_tx = pyro.sample(\"l_tx\", dist.Uniform(0, 1000))\n",
    "    \n",
    "    # Priors\n",
    "    p_wp = dist.Normal(0, l_p**2)\n",
    "    p_w0 = dist.Normal(0, l_0**2)\n",
    "    p_wx = dist.Normal(np.zeros(d), l_x**2 * np.ones(d))\n",
    "    p_wt = dist.Normal(0, l_t**2)\n",
    "    p_twx = dist.Normal(np.zeros(d), l_tx**2 * np.ones(d))\n",
    "    \n",
    "    # Model weights\n",
    "    w_p = pyro.sample(\"propensity\", p_wp)\n",
    "    w_0 = pyro.sample(\"intercept\", p_w0)\n",
    "    w_t = pyro.sample(\"treatment\", p_wt)\n",
    "    w_x = pyro.sample(\"confounders\", p_wx)\n",
    "    w_tx = pyro.sample(\"intersection\", p_twx)\n",
    "    \n",
    "    # Likelihood\n",
    "    pf = predict(w_0, w_t, w_x, w_tx, w_p, xp, xt, t, p)\n",
    "    \n",
    "    with pyro.plate(\"data\", n):\n",
    "        likelihood = dist.Bernoulli(pf)\n",
    "        y = pyro.sample(\"likelihood\", likelihood, obs=y)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "24",
   "metadata": {},
   "source": [
    "### Run MCMC inference to compute the posteriors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "25",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|██████████| 6000/6000 [05:58<00:00, 16.74it/s, 63 steps of size 4.63e-02. acc. prob=0.94] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                      mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "  confounders[0]      0.01      0.05      0.01     -0.06      0.09    912.67      1.00\n",
      "  confounders[1]     -0.04      0.05     -0.04     -0.12      0.04   1172.17      1.00\n",
      "  confounders[2]      0.04      0.05      0.04     -0.04      0.12   1169.71      1.00\n",
      "  confounders[3]      0.08      0.05      0.08      0.01      0.16   1191.39      1.00\n",
      "  confounders[4]      0.04      0.05      0.04     -0.04      0.11   1215.77      1.00\n",
      "  confounders[5]      0.04      0.04      0.04     -0.03      0.10   1244.47      1.00\n",
      "  confounders[6]      0.03      0.04      0.03     -0.04      0.10   1108.99      1.00\n",
      "  confounders[7]     -0.00      0.04     -0.00     -0.07      0.06   1112.92      1.00\n",
      "  confounders[8]      0.06      0.04      0.07     -0.00      0.13    958.63      1.00\n",
      "  confounders[9]      0.02      0.05      0.02     -0.05      0.10   1074.30      1.00\n",
      " confounders[10]      0.01      0.05      0.01     -0.08      0.10    922.90      1.00\n",
      " confounders[11]      0.07      0.05      0.07     -0.01      0.14    855.03      1.00\n",
      " confounders[12]     -0.07      0.04     -0.07     -0.14      0.00    762.16      1.00\n",
      " confounders[13]     -0.01      0.04     -0.01     -0.08      0.06   1198.47      1.00\n",
      " confounders[14]      0.02      0.04      0.02     -0.06      0.08   1110.39      1.00\n",
      " confounders[15]      0.01      0.05      0.01     -0.07      0.10    917.78      1.00\n",
      " confounders[16]      0.04      0.04      0.04     -0.02      0.11   1218.78      1.00\n",
      " confounders[17]     -0.01      0.05     -0.00     -0.08      0.08   1171.37      1.00\n",
      " confounders[18]     -0.04      0.05     -0.04     -0.12      0.05   1316.06      1.00\n",
      " confounders[19]     -0.00      0.05      0.00     -0.08      0.07   1332.24      1.00\n",
      " confounders[20]      0.00      0.05      0.00     -0.08      0.07   1217.48      1.00\n",
      " confounders[21]     -0.03      0.06     -0.03     -0.13      0.06   1037.23      1.00\n",
      " confounders[22]     -0.00      0.05     -0.00     -0.08      0.08   1484.05      1.00\n",
      " confounders[23]     -0.03      0.05     -0.03     -0.11      0.04   1111.24      1.00\n",
      " confounders[24]     -0.04      0.06     -0.04     -0.13      0.06   1115.35      1.00\n",
      " confounders[25]      0.03      0.05      0.03     -0.04      0.12   1194.28      1.00\n",
      " confounders[26]      0.08      0.05      0.08      0.00      0.16    892.33      1.00\n",
      " confounders[27]      0.03      0.05      0.03     -0.05      0.10   1316.57      1.00\n",
      " confounders[28]     -0.03      0.05     -0.03     -0.11      0.06    956.38      1.00\n",
      " confounders[29]     -0.00      0.05      0.00     -0.09      0.08    957.91      1.00\n",
      " confounders[30]      0.04      0.04      0.04     -0.04      0.10    888.66      1.00\n",
      " confounders[31]      0.01      0.05      0.01     -0.08      0.09   1108.07      1.00\n",
      " confounders[32]     -0.03      0.04     -0.03     -0.10      0.04   1145.46      1.00\n",
      " confounders[33]      0.03      0.04      0.03     -0.05      0.10   1185.48      1.00\n",
      " confounders[34]     -0.03      0.04     -0.03     -0.10      0.04   1012.92      1.00\n",
      " confounders[35]      0.00      0.04      0.00     -0.07      0.07   1339.71      1.00\n",
      " confounders[36]     -0.00      0.04     -0.00     -0.08      0.07   1214.45      1.00\n",
      " confounders[37]     -0.06      0.05     -0.06     -0.14      0.04   1048.29      1.00\n",
      " confounders[38]     -0.00      0.05     -0.00     -0.08      0.07   1371.36      1.00\n",
      " confounders[39]     -0.01      0.05     -0.01     -0.10      0.06   1156.52      1.00\n",
      " confounders[40]      0.05      0.04      0.04     -0.02      0.12   1058.65      1.00\n",
      " confounders[41]      0.04      0.05      0.03     -0.03      0.11   1311.41      1.00\n",
      " confounders[42]      0.06      0.04      0.06     -0.00      0.12   1019.67      1.00\n",
      " confounders[43]      0.02      0.04      0.02     -0.05      0.09   1333.72      1.00\n",
      " confounders[44]     -0.11      0.05     -0.11     -0.18     -0.03    812.28      1.00\n",
      " confounders[45]     -0.05      0.05     -0.04     -0.13      0.03   1094.90      1.00\n",
      " confounders[46]      0.07      0.05      0.07      0.00      0.15    984.17      1.00\n",
      " confounders[47]      0.01      0.05      0.01     -0.06      0.09   1064.21      1.00\n",
      " confounders[48]      0.03      0.04      0.03     -0.04      0.08    919.48      1.00\n",
      " confounders[49]      0.07      0.05      0.07     -0.01      0.15   1213.24      1.00\n",
      " confounders[50]     -0.02      0.05     -0.02     -0.10      0.06   1460.76      1.00\n",
      " confounders[51]     -0.03      0.05     -0.03     -0.11      0.05    882.65      1.00\n",
      " confounders[52]     -0.05      0.05     -0.05     -0.13      0.02    744.15      1.00\n",
      " confounders[53]     -0.02      0.05     -0.02     -0.11      0.05    862.93      1.00\n",
      " confounders[54]     -0.01      0.05     -0.01     -0.09      0.06   1392.99      1.00\n",
      " confounders[55]      0.07      0.04      0.07      0.01      0.14   1546.88      1.00\n",
      " confounders[56]      0.01      0.05      0.01     -0.06      0.09   1296.03      1.00\n",
      " confounders[57]      0.06      0.05      0.05     -0.02      0.14   1368.08      1.00\n",
      " confounders[58]      0.10      0.05      0.10      0.02      0.17   1149.10      1.00\n",
      " confounders[59]      0.03      0.04      0.03     -0.05      0.09   1216.08      1.00\n",
      " confounders[60]      0.05      0.04      0.05     -0.02      0.12   1131.70      1.00\n",
      " confounders[61]      0.01      0.04      0.01     -0.06      0.09   1220.64      1.00\n",
      " confounders[62]     -0.04      0.05     -0.03     -0.12      0.04    814.29      1.00\n",
      " confounders[63]     -0.01      0.04     -0.01     -0.09      0.05   1029.90      1.00\n",
      " confounders[64]     -0.04      0.05     -0.04     -0.13      0.03   1188.57      1.00\n",
      " confounders[65]     -0.02      0.05     -0.02     -0.09      0.07   1137.40      1.00\n",
      " confounders[66]      0.04      0.04      0.05     -0.02      0.12    966.19      1.00\n",
      " confounders[67]     -0.05      0.05     -0.05     -0.12      0.04   1313.85      1.00\n",
      " confounders[68]     -0.03      0.05     -0.02     -0.09      0.06   1038.25      1.00\n",
      " confounders[69]     -0.00      0.05     -0.00     -0.08      0.08   1187.92      1.00\n",
      " confounders[70]     -0.09      0.06     -0.10     -0.18      0.01    988.89      1.00\n",
      " confounders[71]     -0.04      0.05     -0.04     -0.12      0.04    644.07      1.01\n",
      " confounders[72]     -0.06      0.06     -0.06     -0.16      0.02    821.91      1.00\n",
      " confounders[73]     -0.08      0.05     -0.08     -0.16      0.02   1045.40      1.00\n",
      " confounders[74]     -0.04      0.05     -0.04     -0.12      0.04   1164.20      1.00\n",
      " confounders[75]      0.03      0.04      0.03     -0.04      0.10   1131.87      1.00\n",
      " confounders[76]     -0.03      0.05     -0.03     -0.11      0.04   1161.14      1.00\n",
      " confounders[77]      0.06      0.05      0.06     -0.03      0.15   1046.87      1.00\n",
      " confounders[78]     -0.07      0.06     -0.07     -0.18      0.01    848.62      1.00\n",
      " confounders[79]     -0.03      0.05     -0.03     -0.10      0.05   1202.81      1.00\n",
      " confounders[80]     -0.05      0.06     -0.05     -0.15      0.04    969.20      1.00\n",
      " confounders[81]      0.05      0.03      0.05     -0.00      0.11    901.68      1.00\n",
      " confounders[82]      0.05      0.05      0.05     -0.05      0.12    967.83      1.00\n",
      " confounders[83]     -0.03      0.05     -0.03     -0.11      0.05    805.74      1.00\n",
      " confounders[84]     -0.04      0.05     -0.03     -0.12      0.04    972.22      1.00\n",
      " confounders[85]      0.05      0.05      0.06     -0.03      0.13   1396.12      1.00\n",
      " confounders[86]     -0.00      0.05     -0.00     -0.07      0.09   1251.88      1.00\n",
      " confounders[87]     -0.04      0.05     -0.04     -0.12      0.03   1192.13      1.00\n",
      " confounders[88]      0.07      0.05      0.07     -0.00      0.14    931.09      1.00\n",
      " confounders[89]      0.05      0.04      0.05     -0.02      0.12   1245.32      1.00\n",
      " confounders[90]     -0.01      0.04     -0.01     -0.08      0.05    958.68      1.00\n",
      "       intercept     -3.16      0.09     -3.16     -3.29     -3.01    612.51      1.00\n",
      " intersection[0]      0.01      0.03      0.00     -0.03      0.04    933.77      1.00\n",
      " intersection[1]      0.01      0.03      0.00     -0.03      0.05     81.49      1.00\n",
      " intersection[2]     -0.00      0.03     -0.00     -0.05      0.03   1458.60      1.00\n",
      " intersection[3]     -0.01      0.03     -0.00     -0.04      0.03    624.23      1.00\n",
      " intersection[4]      0.01      0.03      0.00     -0.03      0.05    431.78      1.00\n",
      " intersection[5]     -0.00      0.02     -0.00     -0.03      0.04   1044.48      1.00\n",
      " intersection[6]     -0.01      0.03     -0.00     -0.06      0.04    186.17      1.00\n",
      " intersection[7]      0.00      0.03      0.00     -0.04      0.04   1539.81      1.00\n",
      " intersection[8]      0.00      0.02     -0.00     -0.03      0.05   1718.12      1.00\n",
      " intersection[9]     -0.01      0.02     -0.00     -0.04      0.04    172.03      1.00\n",
      "intersection[10]      0.01      0.03      0.00     -0.03      0.05    237.86      1.00\n",
      "intersection[11]     -0.00      0.03     -0.00     -0.04      0.04    856.99      1.00\n",
      "intersection[12]     -0.01      0.03     -0.01     -0.06      0.03     52.05      1.00\n",
      "intersection[13]      0.00      0.03      0.00     -0.04      0.05    817.96      1.00\n",
      "intersection[14]      0.01      0.03      0.00     -0.03      0.04    358.85      1.00\n",
      "intersection[15]     -0.00      0.03     -0.00     -0.04      0.04    975.59      1.00\n",
      "intersection[16]     -0.01      0.03     -0.00     -0.05      0.04    652.73      1.00\n",
      "intersection[17]      0.01      0.03      0.00     -0.04      0.05    569.26      1.00\n",
      "intersection[18]     -0.00      0.02     -0.00     -0.05      0.03   1401.82      1.00\n",
      "intersection[19]      0.01      0.03      0.00     -0.03      0.05    106.16      1.00\n",
      "intersection[20]      0.00      0.03      0.00     -0.03      0.04   1040.99      1.00\n",
      "intersection[21]      0.01      0.02      0.00     -0.03      0.05   1059.08      1.00\n",
      "intersection[22]     -0.00      0.03      0.00     -0.04      0.04   1194.43      1.00\n",
      "intersection[23]      0.00      0.03      0.00     -0.03      0.05   1211.66      1.00\n",
      "intersection[24]      0.00      0.03      0.00     -0.04      0.05    932.36      1.00\n",
      "intersection[25]      0.01      0.03      0.00     -0.03      0.04    136.76      1.00\n",
      "intersection[26]      0.01      0.03      0.01     -0.03      0.05    127.04      1.00\n",
      "intersection[27]      0.01      0.03      0.00     -0.03      0.05    246.47      1.00\n",
      "intersection[28]      0.01      0.03      0.01     -0.04      0.06    166.40      1.00\n",
      "intersection[29]     -0.00      0.03     -0.00     -0.05      0.04   1609.39      1.00\n",
      "intersection[30]      0.00      0.03      0.00     -0.04      0.05   1546.19      1.00\n",
      "intersection[31]      0.01      0.03      0.00     -0.03      0.05    713.16      1.00\n",
      "intersection[32]     -0.01      0.03     -0.00     -0.04      0.04    494.94      1.00\n",
      "intersection[33]     -0.00      0.03     -0.00     -0.04      0.04    792.48      1.00\n",
      "intersection[34]      0.00      0.02      0.00     -0.04      0.04   1388.23      1.00\n",
      "intersection[35]      0.00      0.03     -0.00     -0.04      0.05   1292.67      1.00\n",
      "intersection[36]      0.01      0.03      0.00     -0.03      0.05    124.31      1.00\n",
      "intersection[37]     -0.00      0.03     -0.00     -0.04      0.04   1844.30      1.00\n",
      "intersection[38]      0.00      0.03     -0.00     -0.04      0.05   1085.35      1.00\n",
      "intersection[39]     -0.00      0.03     -0.00     -0.04      0.04   1665.31      1.00\n",
      "intersection[40]     -0.01      0.03     -0.00     -0.05      0.03    100.10      1.00\n",
      "intersection[41]     -0.01      0.02     -0.00     -0.05      0.03    304.15      1.00\n",
      "intersection[42]     -0.00      0.03     -0.00     -0.04      0.04   1406.51      1.00\n",
      "intersection[43]      0.01      0.03      0.00     -0.04      0.05    776.64      1.00\n",
      "intersection[44]      0.00      0.02      0.00     -0.03      0.04   1734.64      1.00\n",
      "intersection[45]      0.00      0.03      0.00     -0.04      0.05   1246.10      1.00\n",
      "intersection[46]     -0.01      0.03     -0.00     -0.06      0.04    615.22      1.00\n",
      "intersection[47]     -0.01      0.03     -0.00     -0.05      0.03    304.29      1.00\n",
      "intersection[48]     -0.00      0.03     -0.00     -0.03      0.05   1229.51      1.00\n",
      "intersection[49]      0.01      0.02      0.00     -0.03      0.05    208.05      1.00\n",
      "intersection[50]      0.00      0.03      0.00     -0.04      0.05   1017.58      1.00\n",
      "intersection[51]      0.00      0.03     -0.00     -0.04      0.05   2074.92      1.00\n",
      "intersection[52]     -0.01      0.03     -0.00     -0.06      0.03    498.31      1.00\n",
      "intersection[53]     -0.00      0.03      0.00     -0.04      0.04   1334.85      1.00\n",
      "intersection[54]     -0.00      0.03     -0.00     -0.04      0.04   1489.88      1.00\n",
      "intersection[55]     -0.00      0.03     -0.00     -0.05      0.03    768.90      1.00\n",
      "intersection[56]     -0.00      0.03     -0.00     -0.05      0.03   1008.13      1.00\n",
      "intersection[57]     -0.01      0.03     -0.00     -0.05      0.03    111.45      1.00\n",
      "intersection[58]     -0.01      0.03     -0.00     -0.04      0.04   1593.13      1.00\n",
      "intersection[59]      0.01      0.03      0.00     -0.04      0.05    259.25      1.00\n",
      "intersection[60]      0.01      0.03      0.00     -0.03      0.05    199.01      1.00\n",
      "intersection[61]      0.01      0.03      0.00     -0.02      0.05     99.07      1.00\n",
      "intersection[62]     -0.00      0.03     -0.00     -0.05      0.03   1219.58      1.00\n",
      "intersection[63]     -0.00      0.03     -0.00     -0.05      0.03    441.07      1.00\n",
      "intersection[64]      0.00      0.03      0.00     -0.04      0.04   1183.31      1.00\n",
      "intersection[65]      0.00      0.03      0.00     -0.05      0.04   1605.65      1.00\n",
      "intersection[66]     -0.00      0.03     -0.00     -0.05      0.03    754.01      1.00\n",
      "intersection[67]     -0.01      0.03     -0.01     -0.06      0.03     92.57      1.00\n",
      "intersection[68]      0.01      0.03      0.00     -0.04      0.06    327.76      1.00\n",
      "intersection[69]     -0.00      0.02     -0.00     -0.04      0.03    641.56      1.01\n",
      "intersection[70]     -0.00      0.03     -0.00     -0.05      0.03   1508.78      1.00\n",
      "intersection[71]      0.00      0.02      0.00     -0.04      0.04   1215.47      1.00\n",
      "intersection[72]     -0.00      0.03     -0.00     -0.04      0.04    987.50      1.00\n",
      "intersection[73]      0.00      0.03      0.00     -0.04      0.04   1705.36      1.00\n",
      "intersection[74]     -0.00      0.03     -0.00     -0.04      0.04   1091.94      1.00\n",
      "intersection[75]      0.01      0.03      0.01     -0.03      0.05     93.14      1.00\n",
      "intersection[76]     -0.01      0.03     -0.00     -0.05      0.03    386.37      1.00\n",
      "intersection[77]      0.00      0.03      0.00     -0.04      0.04   1911.54      1.00\n",
      "intersection[78]     -0.00      0.02     -0.00     -0.04      0.04   1302.28      1.00\n",
      "intersection[79]     -0.01      0.03     -0.00     -0.05      0.04    362.33      1.00\n",
      "intersection[80]     -0.00      0.03     -0.00     -0.05      0.03    433.60      1.00\n",
      "intersection[81]     -0.01      0.03     -0.01     -0.05      0.03     61.57      1.00\n",
      "intersection[82]      0.00      0.03     -0.00     -0.04      0.04   1138.23      1.00\n",
      "intersection[83]      0.00      0.03      0.00     -0.04      0.04   1669.29      1.00\n",
      "intersection[84]     -0.00      0.03     -0.00     -0.04      0.04   1460.43      1.00\n",
      "intersection[85]     -0.00      0.03     -0.00     -0.04      0.04   1391.43      1.00\n",
      "intersection[86]      0.01      0.03      0.00     -0.03      0.06    149.75      1.00\n",
      "intersection[87]      0.00      0.03      0.00     -0.04      0.05   1388.42      1.00\n",
      "intersection[88]      0.01      0.03      0.01     -0.03      0.07     50.54      1.00\n",
      "intersection[89]      0.01      0.03      0.00     -0.03      0.05    429.86      1.00\n",
      "intersection[90]      0.01      0.03      0.00     -0.04      0.04    223.05      1.00\n",
      "             l_0      6.35      8.44      3.34      1.02     14.29    369.36      1.00\n",
      "             l_p      2.85      5.88      1.08      0.10      6.30    371.95      1.00\n",
      "             l_t      2.40     10.25      0.81      0.06      3.50    650.63      1.00\n",
      "            l_tx      0.14      0.05      0.13      0.08      0.23     14.84      1.00\n",
      "             l_x      0.25      0.02      0.25      0.23      0.28    267.17      1.00\n",
      "      propensity      0.46      0.53      0.39     -0.27      1.39    664.37      1.00\n",
      "       treatment      0.22      0.14      0.23     -0.02      0.43    662.30      1.00\n",
      "\n",
      "Number of divergences: 33\n"
     ]
    }
   ],
   "source": [
    "samples = 1000\n",
    "warm_up = 5000\n",
    "\n",
    "# Initialize No U-Turn Sampler\n",
    "kernel = NUTS(model_treatment_intersection, max_tree_depth=10)\n",
    "model_mcmc = MCMC(kernel, num_samples=samples, num_warmup=warm_up, num_chains=1)\n",
    "\n",
    "# Run the sampler\n",
    "rng_key = random.PRNGKey(0)\n",
    "model_mcmc.run(rng_key, X, X, t, p, y)\n",
    "model_mcmc.print_summary()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "26",
   "metadata": {},
   "source": [
    "### Sample the ATE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "27",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hierarchical Logistic Regression\n",
      "  Balanced accuracy = 0.5017 (0.0016)\n",
      "  ATE: 0.0124\n",
      "  CI (0.025, 0.975): [-0.0002, 0.0277]\n"
     ]
    }
   ],
   "source": [
    "hbr_samples = model_mcmc.get_samples()\n",
    "w_0s = hbr_samples[\"intercept\"]\n",
    "w_ps = hbr_samples[\"propensity\"]\n",
    "w_ts = hbr_samples[\"treatment\"]\n",
    "w_xs = hbr_samples[\"confounders\"]\n",
    "w_txs = hbr_samples[\"intersection\"]\n",
    "\n",
    "ate_hlr_samples = np.zeros(samples)\n",
    "score_samples = np.zeros(samples)\n",
    "\n",
    "for s in range(samples):\n",
    "    pf = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], X, X, t, p)\n",
    "    y_hat = (pf >= 0.5).astype(int)\n",
    "    pf1 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], X, X, 1, p)\n",
    "    pf0 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], X, X, 0, p)\n",
    "    ate_hlr_samples[s] = (pf1 - pf0).mean()\n",
    "    score_samples[s] = balanced_accuracy_score(y, y_hat)\n",
    "\n",
    "ate_hlr = ate_hlr_samples.mean()\n",
    "ci_hlr = mstats.mquantiles(ate_hlr_samples, prob=[0.025, 0.975])\n",
    "\n",
    "print(\"Hierarchical Logistic Regression\")\n",
    "print(f\"  Balanced accuracy = {score_samples.mean():.4f} ({score_samples.std():.4f})\")\n",
    "print(f\"  ATE: {ate_hlr:.4f}\")\n",
    "print(f\"  CI (0.025, 0.975): [{ci_hlr[0]:.4f}, {ci_hlr[1]:.4f}]\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "cf9ed71e",
   "metadata": {},
   "source": [
    "### Sample and display some posterior distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1ebb279c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posteriors = [\"l_0\", \"l_x\", \"l_p\", \"l_t\", \"l_tx\"]\n",
    "for name in posteriors:\n",
    "    post = hbr_samples[name]\n",
    "    plt.figure(dpi=150)\n",
    "    plt.hist(post, bins=30)\n",
    "    plt.title(name)\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "cnt, *_ = plt.hist(ate_hlr_samples, bins=20)\n",
    "plt.plot([ate_hlr, ate_hlr], [0, max(cnt)], 'r', label=\"mean\")\n",
    "plt.title(\"HLR ATE samples\")\n",
    "plt.xlabel(\"ATE\")\n",
    "plt.ylabel(\"counts\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ca93c5bd",
   "metadata": {},
   "source": [
    "# HLM with Nystroem features\n",
    "\n",
    "This is the same model as the HLM as before, but with a non-linear Nystroem approximation applied to the controls that approximates a Gaussian process radial basis kernel. We use length-scales based on those found by the Gaussian process classifier for the income target.\n",
    "\n",
    "The treatment and prognostic components now become:\n",
    "$$\n",
    "\\begin{align}\n",
    "    \\tau(\\mathbf{x}_i) &= \\mathbf{w}_{tx}^\\top\\phi_{100}(\\mathbf{x}_i) + w_t\\\\\n",
    "    \\rho(\\mathbf{x}_i, \\pi_i) &= w_0 + w_\\pi \\pi_i + \\mathbf{w}_x^\\top\\phi_{10}(\\mathbf{x}_i)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "where $\\phi_l(\\cdot)$ is the Nystroem basis where $l$ indicates the length scale. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6a9be563",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|██████████| 6000/6000 [2:34:02<00:00,  1.54s/it, 1023 steps of size 3.52e-02. acc. prob=0.84]  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                       mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "   confounders[0]      0.03      1.02      0.01     -1.61      1.80    799.92      1.00\n",
      "   confounders[1]      0.14      0.98      0.13     -1.36      1.82    830.02      1.00\n",
      "   confounders[2]     -0.03      0.91     -0.02     -1.75      1.25   1088.56      1.00\n",
      "   confounders[3]      0.21      1.01      0.19     -1.38      1.72    915.73      1.00\n",
      "   confounders[4]     -0.71      0.92     -0.70     -2.18      0.85    944.67      1.00\n",
      "   confounders[5]      0.23      0.99      0.21     -1.35      1.81    898.43      1.00\n",
      "   confounders[6]      0.38      1.05      0.37     -1.32      2.13    847.03      1.00\n",
      "   confounders[7]      0.17      0.95      0.16     -1.20      1.77    886.67      1.00\n",
      "   confounders[8]     -0.70      1.02     -0.64     -2.39      1.00    913.54      1.00\n",
      "   confounders[9]      0.36      0.93      0.38     -1.12      1.94    979.26      1.00\n",
      "  confounders[10]     -0.51      0.97     -0.51     -1.99      1.11    945.87      1.00\n",
      "  confounders[11]      0.17      0.99      0.14     -1.47      1.67    883.20      1.00\n",
      "  confounders[12]      0.05      0.99      0.05     -1.60      1.59    926.73      1.00\n",
      "  confounders[13]     -0.18      0.99     -0.19     -2.09      1.25    884.59      1.00\n",
      "  confounders[14]      0.07      0.92      0.05     -1.33      1.75    896.60      1.00\n",
      "  confounders[15]     -0.51      1.08     -0.47     -2.41      1.07    977.77      1.00\n",
      "  confounders[16]      0.77      0.94      0.80     -0.55      2.51    450.58      1.00\n",
      "  confounders[17]     -0.09      0.95     -0.07     -1.61      1.54    911.36      1.00\n",
      "  confounders[18]      0.36      0.98      0.39     -1.29      1.90   1045.05      1.00\n",
      "  confounders[19]     -0.57      1.06     -0.52     -2.07      1.40    819.54      1.00\n",
      "  confounders[20]     -0.05      1.03     -0.09     -1.46      1.85   1134.42      1.00\n",
      "  confounders[21]      0.96      0.99      0.96     -0.76      2.47    743.72      1.00\n",
      "  confounders[22]     -0.35      1.03     -0.33     -2.03      1.30    909.44      1.00\n",
      "  confounders[23]     -0.22      1.00     -0.27     -1.83      1.42   1025.60      1.00\n",
      "  confounders[24]     -0.38      0.98     -0.35     -1.93      1.15   1072.94      1.00\n",
      "  confounders[25]      0.28      1.03      0.34     -1.33      2.09    817.25      1.00\n",
      "  confounders[26]      0.20      1.00      0.20     -1.40      1.81    657.62      1.00\n",
      "  confounders[27]     -0.39      0.99     -0.34     -2.14      1.03    907.68      1.00\n",
      "  confounders[28]     -0.53      1.05     -0.53     -2.05      1.48   1006.64      1.00\n",
      "  confounders[29]     -0.27      1.06     -0.21     -2.12      1.33    831.45      1.00\n",
      "  confounders[30]     -0.20      1.02     -0.18     -1.71      1.67    714.54      1.00\n",
      "  confounders[31]      0.54      0.97      0.51     -0.90      2.26    921.23      1.00\n",
      "  confounders[32]      0.81      1.03      0.79     -1.03      2.37    955.42      1.00\n",
      "  confounders[33]     -0.45      1.03     -0.50     -2.12      1.17   1060.82      1.00\n",
      "  confounders[34]      0.79      0.97      0.77     -0.86      2.27    806.11      1.00\n",
      "  confounders[35]      0.16      0.97      0.17     -1.45      1.64    959.99      1.00\n",
      "  confounders[36]     -0.16      1.01     -0.12     -1.84      1.39   1037.30      1.00\n",
      "  confounders[37]     -0.56      1.03     -0.59     -2.17      1.10    926.14      1.00\n",
      "  confounders[38]     -0.16      0.98     -0.23     -1.58      1.58    754.08      1.00\n",
      "  confounders[39]     -0.53      1.02     -0.56     -2.09      1.25   1109.40      1.00\n",
      "  confounders[40]     -0.38      1.07     -0.41     -1.91      1.55   1063.72      1.00\n",
      "  confounders[41]      0.15      1.00      0.13     -1.41      1.92    956.78      1.00\n",
      "  confounders[42]      0.33      0.98      0.32     -1.30      1.94   1026.69      1.00\n",
      "  confounders[43]     -0.31      1.01     -0.31     -2.02      1.27    788.10      1.00\n",
      "  confounders[44]      0.38      1.03      0.38     -1.22      2.17   1010.88      1.00\n",
      "  confounders[45]     -0.07      1.06     -0.08     -1.83      1.69    942.67      1.00\n",
      "  confounders[46]     -0.33      1.02     -0.30     -1.90      1.36   1147.23      1.00\n",
      "  confounders[47]      0.25      0.99      0.24     -1.28      1.97    918.97      1.00\n",
      "  confounders[48]      0.05      0.97      0.08     -1.51      1.65    929.57      1.00\n",
      "  confounders[49]     -0.11      0.98     -0.09     -1.81      1.41    836.05      1.00\n",
      "  confounders[50]     -0.13      0.99     -0.11     -1.82      1.44    749.87      1.00\n",
      "  confounders[51]     -0.45      0.96     -0.42     -2.02      1.04    800.00      1.00\n",
      "  confounders[52]     -0.14      1.00     -0.15     -1.73      1.51   1049.19      1.00\n",
      "  confounders[53]     -0.23      1.01     -0.24     -1.87      1.39   1120.04      1.00\n",
      "  confounders[54]     -0.63      1.02     -0.62     -2.04      1.14    836.54      1.00\n",
      "  confounders[55]      0.14      1.01      0.13     -1.48      1.75    970.08      1.00\n",
      "  confounders[56]      1.27      0.96      1.23     -0.16      2.93    492.50      1.00\n",
      "  confounders[57]     -0.09      1.01     -0.11     -1.75      1.53    938.94      1.00\n",
      "  confounders[58]     -0.28      1.06     -0.25     -1.94      1.53   1083.67      1.00\n",
      "  confounders[59]     -0.05      1.03     -0.07     -1.92      1.50    959.91      1.00\n",
      "  confounders[60]      0.16      0.98      0.16     -1.34      1.81    936.02      1.00\n",
      "  confounders[61]     -0.13      1.01     -0.10     -1.79      1.52    973.53      1.00\n",
      "  confounders[62]     -0.47      1.02     -0.46     -2.20      1.15    958.80      1.00\n",
      "  confounders[63]     -0.18      1.02     -0.17     -1.84      1.57    923.07      1.00\n",
      "  confounders[64]     -0.39      1.01     -0.37     -1.85      1.43   1096.67      1.00\n",
      "  confounders[65]     -0.21      0.96     -0.18     -1.68      1.49   1113.65      1.00\n",
      "  confounders[66]     -0.39      1.00     -0.42     -1.88      1.34    954.27      1.00\n",
      "  confounders[67]      0.14      0.99      0.14     -1.44      1.81   1062.58      1.00\n",
      "  confounders[68]     -0.65      1.02     -0.65     -2.25      0.98    990.03      1.00\n",
      "  confounders[69]     -0.37      0.94     -0.36     -1.80      1.24    934.32      1.00\n",
      "  confounders[70]     -0.36      1.00     -0.39     -2.09      1.22    863.95      1.00\n",
      "  confounders[71]     -0.32      1.05     -0.32     -2.08      1.43   1064.81      1.00\n",
      "  confounders[72]     -0.57      1.04     -0.53     -2.17      1.15    852.31      1.00\n",
      "  confounders[73]      0.08      1.01      0.11     -1.56      1.75    818.24      1.00\n",
      "  confounders[74]      0.39      1.03      0.41     -1.16      2.18    918.17      1.00\n",
      "  confounders[75]      0.48      1.02      0.49     -1.11      2.24    851.38      1.00\n",
      "  confounders[76]     -0.40      1.00     -0.39     -1.95      1.32   1055.24      1.00\n",
      "  confounders[77]     -0.33      1.03     -0.32     -2.02      1.38    993.56      1.00\n",
      "  confounders[78]      0.03      1.02      0.01     -1.59      1.60    997.11      1.00\n",
      "  confounders[79]      0.90      0.92      0.87     -0.63      2.35    849.58      1.00\n",
      "  confounders[80]     -0.23      0.92     -0.23     -1.57      1.41   1032.33      1.00\n",
      "  confounders[81]      0.17      1.01      0.24     -1.53      1.71    963.79      1.00\n",
      "  confounders[82]      0.19      0.96      0.17     -1.44      1.77    830.29      1.00\n",
      "  confounders[83]     -0.05      1.07     -0.06     -1.69      1.81    762.69      1.00\n",
      "  confounders[84]     -0.08      0.92     -0.07     -1.64      1.33   1000.26      1.00\n",
      "  confounders[85]     -0.67      1.03     -0.65     -2.78      0.68    928.25      1.00\n",
      "  confounders[86]      0.22      0.94      0.23     -1.31      1.72    852.79      1.00\n",
      "  confounders[87]      0.60      1.02      0.62     -0.95      2.31    766.89      1.00\n",
      "  confounders[88]     -0.36      1.02     -0.32     -2.09      1.22    958.99      1.00\n",
      "  confounders[89]      1.44      1.01      1.39     -0.32      2.94    645.85      1.00\n",
      "  confounders[90]     -0.38      1.03     -0.37     -2.06      1.25    822.05      1.00\n",
      "  confounders[91]      0.16      1.00      0.17     -1.40      1.78    960.05      1.00\n",
      "  confounders[92]     -0.43      1.02     -0.43     -2.01      1.33    959.98      1.00\n",
      "  confounders[93]     -0.13      0.97     -0.12     -1.56      1.61    899.58      1.00\n",
      "  confounders[94]      0.37      0.98      0.38     -1.33      1.89   1131.46      1.00\n",
      "  confounders[95]     -0.01      0.96     -0.02     -1.56      1.51   1130.91      1.00\n",
      "  confounders[96]     -0.32      1.00     -0.36     -1.89      1.28   1125.31      1.00\n",
      "  confounders[97]     -0.02      1.01     -0.02     -1.77      1.52   1123.80      1.00\n",
      "  confounders[98]     -0.14      0.97     -0.14     -1.76      1.42    788.72      1.00\n",
      "  confounders[99]      0.07      1.00     -0.01     -1.66      1.61    777.71      1.00\n",
      " confounders[100]     -0.14      0.97     -0.17     -1.71      1.42   1026.76      1.00\n",
      " confounders[101]      0.37      1.11      0.37     -1.38      2.13    733.76      1.00\n",
      " confounders[102]     -0.52      1.03     -0.53     -2.29      1.09    728.46      1.01\n",
      " confounders[103]     -0.53      0.97     -0.46     -2.33      0.82   1110.13      1.00\n",
      " confounders[104]     -0.13      0.98     -0.15     -1.72      1.45   1020.20      1.00\n",
      " confounders[105]     -0.14      1.01     -0.10     -1.87      1.32    859.19      1.00\n",
      " confounders[106]     -0.60      1.02     -0.55     -2.19      1.12    950.51      1.00\n",
      " confounders[107]     -0.25      0.98     -0.23     -1.73      1.54    913.05      1.00\n",
      " confounders[108]      0.52      1.01      0.52     -1.04      2.30   1076.27      1.00\n",
      " confounders[109]      0.37      1.05      0.36     -1.32      1.99    954.14      1.00\n",
      " confounders[110]     -0.23      0.98     -0.22     -1.69      1.49    932.82      1.00\n",
      " confounders[111]     -0.29      0.98     -0.33     -1.64      1.57    938.98      1.00\n",
      " confounders[112]      0.04      1.01      0.06     -1.67      1.65    713.21      1.00\n",
      " confounders[113]     -0.59      1.06     -0.58     -2.32      1.13    898.67      1.00\n",
      " confounders[114]      0.19      1.04      0.18     -1.40      1.86    931.23      1.00\n",
      " confounders[115]     -0.36      1.04     -0.38     -1.80      1.55    953.88      1.00\n",
      " confounders[116]     -0.02      0.99      0.01     -1.51      1.74   1024.06      1.00\n",
      " confounders[117]     -0.32      0.99     -0.33     -1.86      1.30    964.27      1.00\n",
      " confounders[118]     -0.23      1.00     -0.24     -1.78      1.45    932.61      1.00\n",
      " confounders[119]     -0.05      1.00     -0.05     -1.67      1.54    926.37      1.00\n",
      " confounders[120]     -0.44      0.91     -0.46     -1.85      1.10    895.66      1.00\n",
      " confounders[121]     -0.25      0.98     -0.27     -1.73      1.36    889.68      1.00\n",
      " confounders[122]     -0.03      1.01     -0.03     -1.65      1.55   1105.96      1.00\n",
      " confounders[123]      0.29      0.95      0.29     -1.15      2.08   1026.82      1.00\n",
      " confounders[124]      0.27      0.95      0.27     -1.33      1.78   1055.78      1.00\n",
      " confounders[125]      0.11      1.08      0.09     -1.73      1.83    936.62      1.00\n",
      " confounders[126]     -0.09      0.94     -0.07     -1.87      1.27    776.99      1.00\n",
      " confounders[127]     -0.05      0.98     -0.04     -1.65      1.59   1018.11      1.00\n",
      " confounders[128]      0.60      1.04      0.62     -1.16      2.25    641.47      1.00\n",
      " confounders[129]     -0.11      1.08     -0.12     -1.84      1.69    928.37      1.00\n",
      " confounders[130]      0.75      1.02      0.77     -0.83      2.43    666.11      1.00\n",
      " confounders[131]     -0.16      1.05     -0.12     -1.72      1.72    960.04      1.00\n",
      " confounders[132]      0.58      0.99      0.55     -0.87      2.31    765.72      1.00\n",
      " confounders[133]      0.34      1.06      0.37     -1.41      2.04    826.90      1.00\n",
      " confounders[134]     -0.04      1.01     -0.02     -1.57      1.69   1043.81      1.00\n",
      " confounders[135]     -0.11      1.03     -0.10     -1.85      1.56   1081.67      1.00\n",
      " confounders[136]     -0.45      0.99     -0.44     -2.12      0.95    809.54      1.00\n",
      " confounders[137]      0.28      0.98      0.26     -1.23      1.92    964.38      1.00\n",
      " confounders[138]     -0.11      1.04     -0.14     -1.67      1.57    919.68      1.00\n",
      " confounders[139]      0.04      0.94      0.05     -1.63      1.41   1058.08      1.00\n",
      " confounders[140]     -0.26      1.06     -0.24     -2.02      1.46    812.21      1.00\n",
      " confounders[141]     -0.04      0.97     -0.04     -1.71      1.45    969.62      1.00\n",
      " confounders[142]     -0.19      0.95     -0.18     -1.69      1.32    932.29      1.00\n",
      " confounders[143]      0.35      1.04      0.40     -1.41      2.03    654.05      1.00\n",
      " confounders[144]      1.04      0.90      1.02     -0.42      2.54    632.03      1.00\n",
      " confounders[145]     -0.31      1.01     -0.36     -1.96      1.29    829.50      1.00\n",
      " confounders[146]     -0.16      0.98     -0.14     -1.82      1.30   1003.92      1.00\n",
      " confounders[147]     -0.12      1.03     -0.14     -1.66      1.65    941.77      1.00\n",
      " confounders[148]      0.66      1.01      0.64     -1.23      2.14    981.59      1.00\n",
      " confounders[149]     -0.08      1.00     -0.04     -1.69      1.50    918.16      1.00\n",
      " confounders[150]      0.14      0.99      0.15     -1.53      1.67   1015.82      1.00\n",
      " confounders[151]      0.01      0.93      0.01     -1.48      1.66   1152.65      1.00\n",
      " confounders[152]      0.31      0.96      0.29     -1.27      1.82    887.59      1.00\n",
      " confounders[153]      0.44      1.00      0.41     -1.08      2.08   1100.99      1.00\n",
      " confounders[154]     -0.60      1.04     -0.56     -2.30      1.00    916.63      1.00\n",
      " confounders[155]     -0.53      1.08     -0.56     -2.28      1.20   1119.37      1.00\n",
      " confounders[156]     -0.16      1.10     -0.12     -1.95      1.46   1119.70      1.00\n",
      " confounders[157]     -0.11      1.07     -0.08     -1.81      1.56   1098.86      1.00\n",
      " confounders[158]     -0.23      0.99     -0.23     -1.77      1.42    856.71      1.00\n",
      " confounders[159]     -0.01      0.99      0.02     -1.62      1.58   1070.37      1.00\n",
      " confounders[160]      0.17      1.02      0.20     -1.45      1.81   1085.65      1.00\n",
      " confounders[161]      0.29      1.01      0.28     -1.42      1.91    873.37      1.00\n",
      " confounders[162]     -0.28      1.02     -0.29     -1.78      1.52    729.41      1.00\n",
      " confounders[163]     -0.01      1.02     -0.00     -1.69      1.66    910.78      1.01\n",
      " confounders[164]     -0.49      1.03     -0.46     -2.25      1.14    997.37      1.00\n",
      " confounders[165]     -0.22      0.97     -0.21     -1.85      1.34    899.93      1.00\n",
      " confounders[166]      0.05      0.98      0.06     -1.53      1.62    897.04      1.00\n",
      " confounders[167]     -0.27      1.02     -0.25     -1.82      1.35    898.61      1.00\n",
      " confounders[168]     -0.68      1.02     -0.67     -2.40      0.94   1082.05      1.00\n",
      " confounders[169]      0.22      0.97      0.19     -1.34      1.81   1004.51      1.00\n",
      " confounders[170]     -0.73      1.00     -0.70     -2.38      0.88    992.88      1.00\n",
      " confounders[171]     -0.50      0.98     -0.49     -2.23      0.97   1030.72      1.00\n",
      " confounders[172]      0.05      1.06      0.05     -1.49      1.93    904.68      1.00\n",
      " confounders[173]      0.13      1.06      0.13     -1.53      1.80    690.57      1.00\n",
      " confounders[174]      0.62      1.06      0.57     -1.01      2.37   1134.18      1.00\n",
      " confounders[175]     -0.16      1.06     -0.14     -1.72      1.64    837.73      1.01\n",
      " confounders[176]      0.33      0.96      0.33     -1.26      1.90    734.99      1.00\n",
      " confounders[177]     -0.39      1.08     -0.44     -2.09      1.40    939.08      1.00\n",
      " confounders[178]     -0.57      1.04     -0.60     -2.30      1.12    704.49      1.00\n",
      " confounders[179]      0.16      1.03      0.14     -1.55      1.86    802.74      1.00\n",
      " confounders[180]     -0.26      1.03     -0.28     -1.76      1.60    914.81      1.00\n",
      " confounders[181]     -0.31      1.06     -0.30     -2.11      1.32    795.91      1.00\n",
      " confounders[182]     -0.22      0.99     -0.19     -1.85      1.33   1039.31      1.00\n",
      " confounders[183]      0.24      1.00      0.28     -1.31      1.84    755.58      1.00\n",
      " confounders[184]      0.16      1.06      0.14     -1.57      1.91   1130.30      1.00\n",
      " confounders[185]      0.95      0.79      0.97     -0.24      2.29   1001.00      1.00\n",
      " confounders[186]      0.33      0.91      0.31     -1.35      1.66    903.22      1.00\n",
      " confounders[187]     -0.16      0.98     -0.15     -1.68      1.51   1113.36      1.00\n",
      " confounders[188]     -0.06      0.93     -0.08     -1.53      1.40   1006.19      1.00\n",
      " confounders[189]      0.01      1.08      0.04     -1.71      1.80   1007.58      1.00\n",
      " confounders[190]     -0.14      1.04     -0.15     -1.81      1.55   1060.21      1.00\n",
      " confounders[191]     -0.38      1.00     -0.41     -1.92      1.32    909.35      1.00\n",
      " confounders[192]      0.30      1.01      0.31     -1.46      1.88    904.04      1.00\n",
      " confounders[193]      0.40      0.91      0.39     -1.00      1.93    963.95      1.00\n",
      " confounders[194]     -0.08      1.01     -0.08     -1.68      1.63    995.10      1.00\n",
      " confounders[195]     -0.17      1.03     -0.19     -1.84      1.41   1001.00      1.00\n",
      " confounders[196]     -0.04      1.03     -0.03     -1.58      1.79    812.89      1.00\n",
      " confounders[197]     -0.48      0.97     -0.47     -2.13      0.91    905.30      1.00\n",
      " confounders[198]     -0.22      1.08     -0.26     -1.90      1.51   1194.18      1.00\n",
      " confounders[199]      0.28      1.05      0.26     -1.46      1.97    944.67      1.00\n",
      " confounders[200]     -0.26      0.98     -0.28     -2.00      1.19   1066.02      1.00\n",
      " confounders[201]     -0.08      1.03     -0.11     -1.60      1.66    886.86      1.01\n",
      " confounders[202]      0.38      0.97      0.44     -1.13      2.05    747.80      1.00\n",
      " confounders[203]     -0.34      0.95     -0.31     -1.73      1.34    961.08      1.00\n",
      " confounders[204]     -0.27      1.03     -0.29     -1.88      1.51    994.21      1.00\n",
      " confounders[205]     -0.46      1.01     -0.42     -2.09      1.13   1021.70      1.00\n",
      " confounders[206]      0.01      1.00     -0.01     -1.62      1.63   1168.24      1.00\n",
      " confounders[207]      0.11      1.02      0.12     -1.47      1.87    974.10      1.00\n",
      " confounders[208]     -0.24      1.02     -0.23     -1.95      1.34   1146.64      1.00\n",
      " confounders[209]      0.60      0.97      0.59     -0.98      2.08   1009.24      1.00\n",
      " confounders[210]      0.19      1.00      0.23     -1.50      1.74    757.89      1.00\n",
      " confounders[211]     -0.25      1.01     -0.18     -1.97      1.22    900.76      1.00\n",
      " confounders[212]     -0.08      1.01     -0.09     -1.66      1.65    915.60      1.00\n",
      " confounders[213]     -0.09      0.96     -0.07     -1.80      1.37   1120.47      1.00\n",
      " confounders[214]     -0.50      0.98     -0.47     -2.03      1.20    770.72      1.00\n",
      " confounders[215]     -0.28      1.03     -0.31     -2.02      1.28    794.98      1.00\n",
      " confounders[216]     -0.32      1.03     -0.33     -2.05      1.34   1034.94      1.00\n",
      " confounders[217]     -0.12      0.96     -0.10     -1.73      1.40    929.84      1.00\n",
      " confounders[218]     -0.34      1.05     -0.39     -1.99      1.46   1015.20      1.00\n",
      " confounders[219]      0.14      0.96      0.19     -1.66      1.48   1110.56      1.00\n",
      " confounders[220]      0.16      0.97      0.11     -1.27      1.98   1003.67      1.00\n",
      " confounders[221]     -0.01      0.99     -0.01     -1.71      1.41    841.72      1.00\n",
      " confounders[222]      0.26      0.93      0.28     -1.49      1.54    917.52      1.00\n",
      " confounders[223]      0.55      0.97      0.58     -0.91      2.22    738.29      1.00\n",
      " confounders[224]     -0.48      1.06     -0.45     -2.23      1.21   1064.21      1.00\n",
      " confounders[225]      0.24      0.97      0.26     -1.33      1.75    860.45      1.00\n",
      " confounders[226]     -0.31      0.97     -0.35     -1.91      1.28    999.66      1.00\n",
      " confounders[227]     -0.23      1.03     -0.22     -1.72      1.54   1050.15      1.00\n",
      " confounders[228]     -0.18      1.00     -0.15     -1.88      1.46    950.85      1.00\n",
      " confounders[229]     -0.53      1.04     -0.50     -2.18      1.15   1054.93      1.00\n",
      " confounders[230]     -0.34      0.99     -0.33     -1.82      1.39   1112.63      1.00\n",
      " confounders[231]     -0.32      1.03     -0.30     -2.11      1.26    969.34      1.00\n",
      " confounders[232]      0.03      1.01      0.03     -1.69      1.66   1121.45      1.00\n",
      " confounders[233]      0.36      1.11      0.36     -1.47      1.97    995.38      1.00\n",
      " confounders[234]     -0.12      0.98     -0.10     -1.60      1.58    675.54      1.00\n",
      " confounders[235]     -0.48      1.07     -0.43     -2.34      1.17    819.32      1.00\n",
      " confounders[236]     -0.36      1.02     -0.36     -1.83      1.51    986.15      1.00\n",
      " confounders[237]      0.56      0.95      0.54     -1.02      1.94   1096.81      1.00\n",
      " confounders[238]      0.72      1.04      0.74     -1.04      2.36    763.94      1.00\n",
      " confounders[239]     -0.21      1.02     -0.20     -1.73      1.62   1097.89      1.00\n",
      " confounders[240]     -0.03      1.06     -0.06     -1.85      1.59    862.96      1.00\n",
      " confounders[241]     -0.01      0.98     -0.03     -1.55      1.57    703.26      1.00\n",
      " confounders[242]     -0.35      0.94     -0.31     -1.78      1.28    946.92      1.00\n",
      " confounders[243]      0.02      1.01      0.04     -1.50      1.83   1062.05      1.00\n",
      " confounders[244]     -0.19      1.01     -0.21     -1.75      1.63   1086.03      1.00\n",
      " confounders[245]      0.30      1.04      0.29     -1.28      2.04   1047.07      1.00\n",
      " confounders[246]     -0.75      1.02     -0.70     -2.34      0.92   1024.27      1.00\n",
      " confounders[247]     -0.12      0.98     -0.08     -1.62      1.59    942.65      1.00\n",
      " confounders[248]      0.06      1.06      0.04     -1.65      1.75    946.98      1.00\n",
      " confounders[249]     -0.17      0.99     -0.15     -1.80      1.40    852.21      1.00\n",
      " confounders[250]      0.21      1.07      0.21     -1.57      1.92    914.26      1.00\n",
      " confounders[251]      0.12      1.03      0.16     -1.66      1.68   1034.31      1.00\n",
      " confounders[252]      0.01      0.98      0.03     -1.71      1.42    737.20      1.00\n",
      " confounders[253]      0.21      0.96      0.23     -1.28      1.86    966.28      1.00\n",
      " confounders[254]     -0.41      1.02     -0.34     -1.91      1.36   1141.19      1.00\n",
      " confounders[255]      0.09      0.98      0.11     -1.53      1.60    957.03      1.00\n",
      " confounders[256]     -0.74      1.00     -0.72     -2.29      0.85    610.26      1.00\n",
      " confounders[257]     -0.45      0.95     -0.49     -2.11      1.01    824.87      1.00\n",
      " confounders[258]     -0.32      1.00     -0.33     -1.74      1.49    733.97      1.00\n",
      " confounders[259]     -0.04      1.01     -0.06     -1.66      1.64   1075.88      1.00\n",
      " confounders[260]      0.20      0.95      0.19     -1.41      1.72   1139.70      1.00\n",
      " confounders[261]     -0.07      0.98     -0.04     -1.53      1.60   1071.67      1.00\n",
      " confounders[262]     -0.57      1.05     -0.56     -2.43      0.94    759.67      1.00\n",
      " confounders[263]     -0.44      1.06     -0.45     -2.41      1.07    947.82      1.00\n",
      " confounders[264]      0.00      1.01      0.05     -1.74      1.61    866.71      1.00\n",
      " confounders[265]     -0.10      1.01     -0.10     -1.74      1.55    881.69      1.00\n",
      " confounders[266]      0.74      0.97      0.71     -0.83      2.25    702.87      1.00\n",
      " confounders[267]      0.27      1.04      0.25     -1.51      1.86    952.57      1.00\n",
      " confounders[268]     -0.59      1.05     -0.51     -2.24      1.26    992.53      1.00\n",
      " confounders[269]      0.18      1.07      0.10     -1.64      1.81    998.92      1.01\n",
      " confounders[270]     -0.22      0.95     -0.23     -1.68      1.30   1062.88      1.00\n",
      " confounders[271]      0.07      0.98      0.07     -1.57      1.62   1147.19      1.00\n",
      " confounders[272]     -0.29      0.98     -0.29     -2.00      1.19    939.88      1.00\n",
      " confounders[273]     -0.11      1.00     -0.09     -1.79      1.38   1041.35      1.00\n",
      " confounders[274]     -0.17      0.99     -0.15     -1.69      1.47    979.32      1.00\n",
      " confounders[275]     -0.25      1.05     -0.21     -2.02      1.46   1162.95      1.00\n",
      " confounders[276]      0.03      0.91      0.02     -1.31      1.68   1047.68      1.00\n",
      " confounders[277]     -0.45      1.02     -0.48     -2.13      1.24   1211.77      1.00\n",
      " confounders[278]      0.08      0.97      0.07     -1.48      1.62   1132.36      1.01\n",
      " confounders[279]     -0.20      1.01     -0.18     -1.81      1.44   1017.11      1.00\n",
      " confounders[280]      0.13      1.03      0.12     -1.65      1.81    932.33      1.00\n",
      " confounders[281]     -0.40      1.03     -0.36     -2.24      1.10    873.99      1.00\n",
      " confounders[282]     -0.11      1.01     -0.11     -1.61      1.64    795.29      1.00\n",
      " confounders[283]      0.03      0.95     -0.00     -1.54      1.57   1068.46      1.00\n",
      " confounders[284]     -0.20      0.97     -0.15     -1.66      1.43    737.77      1.00\n",
      " confounders[285]     -0.46      0.99     -0.46     -1.86      1.40    794.55      1.00\n",
      " confounders[286]      0.39      0.95      0.38     -1.07      1.88    962.55      1.00\n",
      " confounders[287]     -0.19      0.95     -0.17     -1.65      1.29    915.94      1.00\n",
      " confounders[288]     -0.52      1.01     -0.51     -2.14      0.96    816.79      1.00\n",
      " confounders[289]      0.59      1.08      0.57     -1.17      2.42   1111.08      1.00\n",
      " confounders[290]      0.28      0.93      0.30     -1.20      1.79   1032.91      1.00\n",
      " confounders[291]     -0.41      1.07     -0.35     -2.02      1.42    989.23      1.00\n",
      " confounders[292]     -0.17      1.00     -0.15     -2.00      1.33    961.94      1.00\n",
      " confounders[293]      0.48      0.98      0.51     -1.35      1.81    859.76      1.00\n",
      " confounders[294]     -0.30      0.98     -0.33     -1.76      1.50    987.76      1.00\n",
      " confounders[295]      0.23      1.08      0.24     -1.48      1.91   1291.51      1.00\n",
      " confounders[296]     -0.01      1.11      0.03     -1.93      1.68    920.40      1.00\n",
      " confounders[297]     -0.19      0.99     -0.23     -1.71      1.51    926.59      1.00\n",
      " confounders[298]     -0.40      1.02     -0.37     -2.05      1.27    951.37      1.00\n",
      " confounders[299]      0.97      1.04      0.98     -0.67      2.50    646.50      1.00\n",
      " confounders[300]      0.29      1.00      0.29     -1.33      1.87    998.96      1.00\n",
      " confounders[301]     -0.03      1.04     -0.02     -1.60      1.80   1045.60      1.00\n",
      " confounders[302]     -0.36      1.01     -0.31     -2.01      1.18    895.39      1.00\n",
      " confounders[303]     -0.35      0.97     -0.37     -1.86      1.32   1056.54      1.00\n",
      " confounders[304]     -0.03      1.01     -0.03     -1.53      1.74    736.52      1.00\n",
      " confounders[305]     -0.07      1.00     -0.03     -1.60      1.57   1033.21      1.00\n",
      " confounders[306]      0.00      0.93     -0.02     -1.50      1.52   1055.42      1.00\n",
      " confounders[307]      0.13      0.95      0.13     -1.35      1.80   1073.87      1.00\n",
      " confounders[308]      0.06      0.99      0.06     -1.48      1.76    969.82      1.00\n",
      " confounders[309]     -0.42      1.03     -0.44     -2.08      1.35   1109.20      1.00\n",
      " confounders[310]      0.16      1.01      0.20     -1.51      1.69   1124.45      1.00\n",
      " confounders[311]      0.19      0.98      0.16     -1.54      1.71    878.47      1.00\n",
      " confounders[312]     -0.24      1.01     -0.24     -1.75      1.40    897.24      1.00\n",
      " confounders[313]      0.36      0.94      0.37     -1.21      1.89    943.45      1.00\n",
      " confounders[314]     -0.30      1.02     -0.27     -1.90      1.36    952.47      1.00\n",
      " confounders[315]      0.25      1.01      0.28     -1.34      1.89    983.30      1.00\n",
      " confounders[316]     -0.32      0.94     -0.31     -1.89      1.19   1090.60      1.00\n",
      " confounders[317]      1.00      0.96      1.03     -0.46      2.75    590.28      1.00\n",
      " confounders[318]      0.04      0.98      0.03     -1.65      1.57   1037.31      1.00\n",
      " confounders[319]     -0.16      1.07     -0.15     -1.90      1.53    843.25      1.00\n",
      " confounders[320]     -0.22      1.02     -0.20     -2.04      1.32    789.82      1.00\n",
      " confounders[321]      0.19      0.97      0.20     -1.38      1.78    847.14      1.00\n",
      " confounders[322]      0.41      0.95      0.36     -1.14      2.02    828.54      1.00\n",
      " confounders[323]     -0.19      1.00     -0.14     -1.90      1.37    932.86      1.00\n",
      " confounders[324]      0.47      0.95      0.47     -1.09      2.00    923.07      1.00\n",
      " confounders[325]     -0.06      1.07     -0.07     -1.99      1.57   1029.70      1.00\n",
      " confounders[326]     -0.04      1.00     -0.06     -1.68      1.60    822.55      1.00\n",
      " confounders[327]     -0.54      1.02     -0.54     -2.17      1.10    886.49      1.00\n",
      " confounders[328]     -0.75      1.02     -0.74     -2.41      0.94    912.51      1.00\n",
      " confounders[329]     -0.08      0.99     -0.08     -1.58      1.48   1008.46      1.00\n",
      " confounders[330]     -0.32      1.07     -0.34     -2.00      1.53    996.50      1.00\n",
      " confounders[331]     -0.12      0.94     -0.11     -1.59      1.40    822.10      1.01\n",
      " confounders[332]     -0.59      1.03     -0.61     -2.03      1.34    787.40      1.00\n",
      " confounders[333]     -0.25      1.04     -0.25     -1.86      1.48    990.56      1.00\n",
      " confounders[334]     -0.28      1.02     -0.26     -1.98      1.32    769.93      1.00\n",
      " confounders[335]     -0.01      1.03     -0.04     -1.84      1.62    908.81      1.00\n",
      " confounders[336]     -0.20      1.01     -0.23     -1.75      1.44    869.13      1.00\n",
      " confounders[337]     -0.16      1.00     -0.15     -1.76      1.54   1089.41      1.00\n",
      " confounders[338]      0.01      1.00      0.03     -1.69      1.64   1184.44      1.00\n",
      " confounders[339]      0.05      1.03      0.04     -1.56      1.76    979.79      1.00\n",
      " confounders[340]     -0.13      0.96     -0.15     -1.63      1.44    887.40      1.00\n",
      " confounders[341]     -0.22      0.95     -0.19     -1.72      1.33    944.47      1.00\n",
      " confounders[342]     -0.69      1.11     -0.69     -2.53      1.09   1150.17      1.00\n",
      " confounders[343]     -0.09      1.05     -0.04     -1.82      1.63    762.45      1.00\n",
      " confounders[344]     -0.12      1.11     -0.10     -1.96      1.65    980.54      1.00\n",
      " confounders[345]     -0.04      1.02     -0.03     -1.60      1.63    984.13      1.00\n",
      " confounders[346]     -0.16      0.93     -0.16     -1.61      1.37   1138.52      1.00\n",
      " confounders[347]      0.15      0.92      0.17     -1.39      1.60   1099.31      1.00\n",
      " confounders[348]     -0.71      0.96     -0.72     -2.32      0.87   1120.96      1.00\n",
      " confounders[349]      0.02      1.02      0.03     -1.54      1.71    873.76      1.00\n",
      " confounders[350]     -0.33      1.06     -0.34     -1.87      1.63    976.33      1.00\n",
      " confounders[351]     -0.35      1.02     -0.37     -2.04      1.33    702.54      1.00\n",
      " confounders[352]     -0.36      1.06     -0.35     -1.97      1.45    963.86      1.00\n",
      " confounders[353]     -0.26      1.01     -0.28     -1.86      1.42    917.68      1.00\n",
      " confounders[354]      0.28      1.01      0.31     -1.33      2.01    890.77      1.00\n",
      " confounders[355]      0.27      1.07      0.24     -1.38      2.17    913.17      1.00\n",
      " confounders[356]     -0.21      0.99     -0.22     -1.59      1.70    914.11      1.00\n",
      " confounders[357]     -0.06      1.03     -0.02     -1.66      1.68    900.22      1.00\n",
      " confounders[358]      0.19      0.93      0.19     -1.24      1.74    897.88      1.00\n",
      " confounders[359]     -0.75      1.06     -0.70     -2.35      1.10    865.61      1.00\n",
      " confounders[360]      0.20      0.95      0.20     -1.29      1.77    979.65      1.00\n",
      " confounders[361]      0.30      0.97      0.30     -1.27      1.78    971.28      1.00\n",
      " confounders[362]      0.34      0.97      0.32     -1.22      1.96   1045.16      1.00\n",
      " confounders[363]      0.33      0.96      0.34     -1.21      1.87    871.67      1.00\n",
      " confounders[364]     -0.38      1.09     -0.37     -2.24      1.31    924.58      1.00\n",
      " confounders[365]     -0.23      1.08     -0.16     -1.83      1.65    881.39      1.01\n",
      " confounders[366]     -0.23      1.03     -0.25     -1.90      1.48   1054.87      1.00\n",
      " confounders[367]     -0.24      1.01     -0.25     -1.60      1.69   1068.51      1.00\n",
      " confounders[368]     -0.04      1.04     -0.03     -1.63      1.80   1041.22      1.00\n",
      " confounders[369]     -0.38      1.01     -0.41     -1.92      1.24    898.24      1.00\n",
      " confounders[370]     -0.44      0.99     -0.43     -1.96      1.28   1023.75      1.00\n",
      " confounders[371]     -0.03      0.95      0.02     -1.45      1.65    677.75      1.00\n",
      " confounders[372]     -0.14      1.03     -0.13     -1.68      1.58   1095.30      1.00\n",
      " confounders[373]     -0.23      1.02     -0.22     -2.16      1.24    910.78      1.00\n",
      " confounders[374]      0.56      1.02      0.57     -1.14      2.29   1147.60      1.00\n",
      " confounders[375]     -0.37      1.03     -0.37     -1.98      1.36    874.39      1.00\n",
      " confounders[376]     -0.09      0.97     -0.11     -1.52      1.54   1206.60      1.00\n",
      " confounders[377]      0.18      0.96      0.19     -1.52      1.64    885.74      1.01\n",
      " confounders[378]     -0.28      1.04     -0.32     -2.07      1.32   1106.07      1.00\n",
      " confounders[379]     -0.17      1.00     -0.18     -1.75      1.52    729.54      1.00\n",
      " confounders[380]     -0.04      1.00     -0.09     -1.66      1.61    778.65      1.00\n",
      " confounders[381]      0.03      0.99      0.04     -1.62      1.54    998.14      1.00\n",
      " confounders[382]     -0.11      0.95     -0.07     -1.61      1.48   1104.13      1.00\n",
      " confounders[383]      0.18      0.98      0.18     -1.42      1.69    887.13      1.00\n",
      " confounders[384]     -0.29      0.99     -0.30     -1.94      1.28    941.06      1.00\n",
      " confounders[385]      0.24      1.04      0.31     -1.41      1.97    933.36      1.00\n",
      " confounders[386]     -0.15      1.02     -0.14     -1.69      1.72    785.10      1.00\n",
      " confounders[387]      0.27      0.97      0.24     -1.31      1.93    842.80      1.00\n",
      " confounders[388]     -0.16      1.03     -0.12     -1.87      1.48    928.26      1.00\n",
      " confounders[389]     -0.18      1.07     -0.19     -1.90      1.61    948.33      1.00\n",
      " confounders[390]     -0.04      0.96     -0.02     -1.63      1.51    982.20      1.00\n",
      " confounders[391]     -0.11      0.99     -0.09     -1.76      1.48   1078.52      1.00\n",
      " confounders[392]     -0.65      1.00     -0.67     -2.34      0.92    745.76      1.00\n",
      " confounders[393]      0.47      0.99      0.48     -1.06      2.10    865.80      1.00\n",
      " confounders[394]     -0.23      0.94     -0.21     -1.85      1.23   1227.07      1.00\n",
      " confounders[395]      0.03      1.00      0.06     -1.52      1.68    900.45      1.00\n",
      " confounders[396]     -0.32      0.98     -0.31     -1.73      1.42    810.39      1.00\n",
      " confounders[397]     -0.37      0.99     -0.34     -1.97      1.20   1074.65      1.00\n",
      " confounders[398]     -0.44      0.99     -0.40     -1.99      1.06    934.70      1.00\n",
      " confounders[399]     -0.55      1.02     -0.53     -2.11      1.23   1085.29      1.00\n",
      " confounders[400]     -0.23      1.06     -0.20     -1.99      1.42    961.83      1.00\n",
      " confounders[401]     -0.17      1.01     -0.16     -1.91      1.44    950.71      1.01\n",
      " confounders[402]      0.25      0.97      0.25     -1.33      1.90    905.00      1.00\n",
      " confounders[403]     -0.26      1.01     -0.24     -1.92      1.37    879.92      1.00\n",
      " confounders[404]     -0.33      1.03     -0.33     -2.00      1.32    919.72      1.00\n",
      " confounders[405]     -0.80      1.06     -0.79     -2.47      0.95   1058.20      1.00\n",
      " confounders[406]     -0.48      1.02     -0.50     -1.96      1.32    727.87      1.00\n",
      " confounders[407]     -0.12      1.09     -0.07     -1.75      1.81    945.52      1.00\n",
      " confounders[408]     -0.09      1.00     -0.09     -1.60      1.68    907.94      1.00\n",
      " confounders[409]     -0.04      0.94     -0.07     -1.55      1.47    941.13      1.00\n",
      " confounders[410]      0.04      1.02      0.06     -1.63      1.68    529.58      1.00\n",
      " confounders[411]     -0.00      0.97      0.01     -1.48      1.71    653.65      1.00\n",
      " confounders[412]     -0.22      0.99     -0.17     -1.75      1.51    712.88      1.00\n",
      " confounders[413]     -0.19      1.06     -0.19     -1.88      1.56    981.29      1.00\n",
      " confounders[414]      0.11      1.04      0.08     -1.43      1.98   1007.50      1.00\n",
      " confounders[415]      0.31      1.02      0.33     -1.48      1.85    842.00      1.00\n",
      " confounders[416]     -0.23      1.01     -0.22     -1.97      1.27    798.62      1.01\n",
      " confounders[417]     -0.56      1.04     -0.53     -2.24      1.06    628.70      1.00\n",
      " confounders[418]     -0.19      0.99     -0.20     -1.75      1.40    747.64      1.00\n",
      " confounders[419]      0.10      1.02      0.10     -1.56      1.70    875.78      1.00\n",
      " confounders[420]     -0.20      1.07     -0.19     -1.86      1.60    842.24      1.00\n",
      " confounders[421]      0.65      1.03      0.65     -1.06      2.27   1083.71      1.00\n",
      " confounders[422]     -0.52      0.97     -0.51     -2.12      1.02    927.51      1.00\n",
      " confounders[423]     -0.06      0.95     -0.03     -1.79      1.42   1026.40      1.00\n",
      " confounders[424]      0.00      0.94      0.01     -1.52      1.53    980.27      1.00\n",
      " confounders[425]      0.57      1.00      0.58     -0.92      2.28   1059.29      1.00\n",
      " confounders[426]     -0.16      0.96     -0.18     -1.69      1.40    887.58      1.01\n",
      " confounders[427]      0.16      0.97      0.16     -1.37      1.82    961.60      1.00\n",
      " confounders[428]     -0.43      1.02     -0.37     -2.03      1.15   1028.51      1.00\n",
      " confounders[429]      0.13      0.92      0.12     -1.34      1.65    936.78      1.00\n",
      " confounders[430]     -0.03      1.02     -0.04     -1.74      1.66   1024.07      1.00\n",
      " confounders[431]      0.10      1.03      0.12     -1.65      1.65   1036.47      1.00\n",
      " confounders[432]      0.18      0.99      0.21     -1.29      1.93    795.29      1.00\n",
      " confounders[433]     -0.53      0.99     -0.52     -2.22      1.05   1044.45      1.00\n",
      " confounders[434]     -0.14      0.98     -0.14     -1.87      1.36    757.44      1.00\n",
      " confounders[435]      0.97      1.07      0.87     -0.60      2.84    531.33      1.00\n",
      " confounders[436]      0.19      0.98      0.16     -1.30      1.77   1100.53      1.00\n",
      " confounders[437]     -0.42      1.09     -0.43     -2.21      1.42    921.46      1.00\n",
      " confounders[438]     -0.34      1.04     -0.39     -2.13      1.26    841.33      1.00\n",
      " confounders[439]      0.13      1.04      0.15     -1.70      1.67    982.47      1.00\n",
      " confounders[440]     -0.68      0.99     -0.64     -2.27      0.87    719.74      1.00\n",
      " confounders[441]      0.19      0.99      0.20     -1.55      1.73    973.16      1.00\n",
      " confounders[442]      0.89      0.98      0.93     -0.73      2.47    503.32      1.00\n",
      " confounders[443]     -0.13      0.95     -0.10     -1.76      1.34   1039.93      1.00\n",
      " confounders[444]      0.80      0.99      0.76     -0.74      2.40    914.44      1.00\n",
      " confounders[445]     -0.06      1.04     -0.05     -1.90      1.47   1054.53      1.00\n",
      " confounders[446]     -0.19      1.11     -0.14     -1.96      1.73    747.50      1.00\n",
      " confounders[447]      0.16      0.94      0.17     -1.47      1.59    953.39      1.00\n",
      " confounders[448]      0.00      0.97      0.03     -1.47      1.75   1021.51      1.00\n",
      " confounders[449]      0.78      0.96      0.78     -0.87      2.22    869.19      1.00\n",
      " confounders[450]     -0.11      1.02     -0.09     -1.75      1.51    911.17      1.00\n",
      " confounders[451]      1.04      0.98      1.04     -0.58      2.51    678.41      1.00\n",
      " confounders[452]     -0.14      0.99     -0.14     -1.82      1.40    963.27      1.00\n",
      " confounders[453]      0.16      1.00      0.18     -1.48      1.79    968.58      1.00\n",
      " confounders[454]      0.39      1.04      0.38     -1.35      2.05    744.94      1.00\n",
      " confounders[455]     -0.27      1.04     -0.30     -2.00      1.43    941.58      1.00\n",
      " confounders[456]      0.03      1.01      0.05     -1.48      1.80   1015.32      1.00\n",
      " confounders[457]     -0.11      0.95     -0.10     -1.85      1.29   1003.46      1.01\n",
      " confounders[458]      0.69      1.08      0.65     -1.12      2.32    627.04      1.00\n",
      " confounders[459]     -0.08      0.92     -0.08     -1.47      1.42   1117.42      1.00\n",
      " confounders[460]      0.46      0.98      0.47     -1.04      2.06    859.06      1.00\n",
      " confounders[461]     -0.17      1.10     -0.17     -1.82      1.84    978.56      1.00\n",
      " confounders[462]     -0.37      0.98     -0.36     -1.98      1.16    782.93      1.00\n",
      " confounders[463]      0.13      0.98      0.17     -1.30      1.85   1086.68      1.00\n",
      " confounders[464]      0.35      0.95      0.39     -1.22      1.85    872.12      1.00\n",
      " confounders[465]     -0.10      0.99     -0.11     -1.53      1.64   1049.51      1.00\n",
      " confounders[466]     -0.57      1.04     -0.56     -2.25      1.08    958.37      1.00\n",
      " confounders[467]      0.36      0.97      0.37     -1.22      1.92    874.12      1.00\n",
      " confounders[468]     -0.33      1.04     -0.33     -1.84      1.47    895.80      1.00\n",
      " confounders[469]      0.53      0.96      0.51     -1.03      2.12    784.97      1.00\n",
      " confounders[470]     -0.07      0.97     -0.08     -1.80      1.40   1008.96      1.00\n",
      " confounders[471]      0.32      0.96      0.33     -1.17      1.98    926.24      1.00\n",
      " confounders[472]      1.21      0.98      1.17     -0.30      2.89    536.63      1.00\n",
      " confounders[473]      0.10      1.03      0.05     -1.65      1.68    755.27      1.00\n",
      " confounders[474]     -0.05      1.02     -0.04     -1.82      1.57   1051.39      1.00\n",
      " confounders[475]      0.47      0.91      0.46     -0.99      1.89    967.07      1.00\n",
      " confounders[476]      0.22      0.95      0.26     -1.24      1.81   1081.74      1.00\n",
      " confounders[477]     -0.13      0.97     -0.14     -1.68      1.49    959.10      1.00\n",
      " confounders[478]     -0.33      0.97     -0.33     -1.97      1.14   1086.45      1.00\n",
      " confounders[479]     -0.83      1.07     -0.81     -2.67      0.81    622.59      1.00\n",
      " confounders[480]     -0.51      1.04     -0.52     -2.00      1.37    838.11      1.00\n",
      " confounders[481]      0.22      0.98      0.20     -1.24      1.91   1007.75      1.00\n",
      " confounders[482]      0.41      0.94      0.43     -1.09      1.93    898.86      1.00\n",
      " confounders[483]     -0.11      1.02     -0.14     -1.79      1.47    931.93      1.00\n",
      " confounders[484]      0.19      0.97      0.23     -1.43      1.68    798.90      1.00\n",
      " confounders[485]      0.30      0.96      0.24     -1.20      2.05    993.76      1.00\n",
      " confounders[486]      0.07      0.96      0.08     -1.47      1.62   1155.83      1.00\n",
      " confounders[487]     -0.31      1.06     -0.35     -2.04      1.52   1035.23      1.00\n",
      " confounders[488]     -0.10      1.04     -0.07     -1.94      1.49   1034.50      1.00\n",
      " confounders[489]      0.13      0.99      0.10     -1.29      1.88   1076.56      1.00\n",
      " confounders[490]     -0.50      1.02     -0.47     -2.09      1.16    586.83      1.00\n",
      " confounders[491]     -0.73      1.01     -0.77     -2.53      0.84    631.88      1.00\n",
      " confounders[492]      0.06      0.95      0.07     -1.55      1.56    540.24      1.00\n",
      " confounders[493]      0.18      0.97      0.17     -1.58      1.58    843.28      1.00\n",
      " confounders[494]     -0.27      1.04     -0.25     -2.07      1.28    850.04      1.00\n",
      " confounders[495]      0.06      1.00      0.06     -1.55      1.65    913.66      1.00\n",
      " confounders[496]     -0.33      0.94     -0.33     -1.75      1.37    925.89      1.00\n",
      " confounders[497]     -0.35      1.00     -0.32     -1.85      1.35   1076.76      1.00\n",
      " confounders[498]      0.02      1.06      0.01     -1.71      1.70    992.61      1.00\n",
      " confounders[499]      0.48      0.98      0.45     -0.97      2.05    950.28      1.00\n",
      "        intercept     -2.57      0.22     -2.57     -2.95     -2.25    674.12      1.01\n",
      "  intersection[0]      0.00      2.24     -0.01     -3.67      3.55    538.92      1.00\n",
      "  intersection[1]      0.08      2.34      0.07     -3.46      3.88    610.46      1.00\n",
      "  intersection[2]     -0.42      2.19     -0.27     -3.92      3.29    536.99      1.03\n",
      "  intersection[3]      0.22      2.26      0.05     -3.05      4.49    851.05      1.00\n",
      "  intersection[4]      0.18      2.24      0.12     -3.30      4.27    754.83      1.00\n",
      "  intersection[5]      0.29      2.40      0.21     -3.06      4.87    691.60      1.00\n",
      "  intersection[6]      0.29      2.37      0.08     -3.23      4.45    451.62      1.01\n",
      "  intersection[7]     -0.28      2.27     -0.18     -3.99      3.44    529.05      1.00\n",
      "  intersection[8]      0.26      2.32      0.20     -3.94      4.09    476.02      1.00\n",
      "  intersection[9]     -0.16      2.18     -0.20     -3.93      3.14    470.95      1.00\n",
      " intersection[10]      0.14      2.23      0.11     -3.59      3.61    582.00      1.00\n",
      " intersection[11]     -0.05      2.32     -0.04     -3.77      3.97    470.74      1.00\n",
      " intersection[12]      0.06      2.43     -0.03     -3.66      4.40    755.03      1.00\n",
      " intersection[13]      0.45      2.19      0.26     -2.99      4.12    710.42      1.03\n",
      " intersection[14]      0.39      2.38      0.23     -3.78      4.17    374.19      1.02\n",
      " intersection[15]     -0.07      2.30     -0.03     -4.47      3.36    684.64      1.00\n",
      " intersection[16]     -0.27      2.38     -0.12     -4.07      3.36    330.19      1.01\n",
      " intersection[17]     -0.22      2.35     -0.09     -4.06      3.52    809.00      1.00\n",
      " intersection[18]      0.72      2.28      0.56     -3.45      3.91    320.47      1.02\n",
      " intersection[19]      0.30      2.37      0.28     -3.85      4.14    561.47      1.00\n",
      " intersection[20]      0.22      2.34      0.22     -3.43      4.26    429.61      1.00\n",
      " intersection[21]     -0.12      2.30     -0.04     -4.19      3.14    588.02      1.00\n",
      " intersection[22]      0.13      2.15      0.08     -3.57      3.42    708.41      1.00\n",
      " intersection[23]     -0.17      2.34     -0.06     -3.69      3.71    439.49      1.00\n",
      " intersection[24]      0.15      2.25      0.07     -3.54      3.95    772.83      1.00\n",
      " intersection[25]     -0.04      2.37      0.08     -3.85      4.12    895.04      1.00\n",
      " intersection[26]     -0.08      2.52     -0.07     -3.82      3.98    669.31      1.00\n",
      " intersection[27]      0.25      2.15      0.23     -3.29      3.71    488.57      1.00\n",
      " intersection[28]     -0.29      2.13     -0.19     -3.50      3.55    608.34      1.01\n",
      " intersection[29]      0.21      2.52      0.09     -3.63      4.87    580.31      1.00\n",
      " intersection[30]      0.14      2.27      0.12     -3.87      3.51    571.08      1.00\n",
      " intersection[31]      0.05      2.31      0.03     -3.62      4.28    440.78      1.00\n",
      " intersection[32]     -0.03      2.38      0.04     -4.52      3.47    564.16      1.00\n",
      " intersection[33]     -0.12      2.33     -0.15     -3.71      4.03    642.05      1.00\n",
      " intersection[34]      0.36      2.29      0.16     -3.08      4.52    689.25      1.01\n",
      " intersection[35]     -0.36      2.38     -0.24     -4.93      3.00    523.63      1.01\n",
      " intersection[36]      0.73      2.35      0.52     -2.61      5.09    581.03      1.02\n",
      " intersection[37]     -0.29      2.43     -0.21     -4.03      3.71    653.89      1.00\n",
      " intersection[38]      0.50      2.39      0.39     -3.26      4.90    646.28      1.01\n",
      " intersection[39]     -0.10      2.25     -0.12     -3.45      4.25    750.47      1.00\n",
      " intersection[40]      0.25      2.35      0.15     -3.73      3.70    517.81      1.01\n",
      " intersection[41]     -0.34      2.37     -0.23     -4.26      3.65    636.52      1.00\n",
      " intersection[42]     -0.27      2.25     -0.25     -4.71      2.94    673.39      1.00\n",
      " intersection[43]     -0.23      2.39     -0.23     -4.00      3.60    632.98      1.01\n",
      " intersection[44]      0.31      2.36      0.16     -4.00      3.82    429.62      1.01\n",
      " intersection[45]     -0.37      2.18     -0.32     -4.27      3.03    465.47      1.01\n",
      " intersection[46]      0.70      2.38      0.52     -3.25      4.17    339.88      1.01\n",
      " intersection[47]      0.18      2.39      0.09     -4.27      3.65    587.77      1.00\n",
      " intersection[48]      0.19      2.42      0.08     -3.76      4.00    557.26      1.00\n",
      " intersection[49]     -0.07      2.19     -0.02     -3.89      3.39    635.84      1.00\n",
      " intersection[50]     -0.25      2.36     -0.22     -4.52      3.34    855.40      1.00\n",
      " intersection[51]      0.26      2.26      0.12     -3.20      4.33    578.73      1.00\n",
      " intersection[52]     -0.06      2.29     -0.05     -3.62      4.23    441.21      1.00\n",
      " intersection[53]      0.16      2.43      0.06     -4.51      3.72    619.70      1.00\n",
      " intersection[54]      0.56      2.27      0.42     -2.77      4.70    485.45      1.01\n",
      " intersection[55]      0.48      2.44      0.25     -3.08      4.53    651.42      1.01\n",
      " intersection[56]     -0.10      2.33     -0.09     -3.69      3.52    579.15      1.00\n",
      " intersection[57]      0.32      2.27      0.08     -3.52      4.04    600.64      1.01\n",
      " intersection[58]      0.04      2.54      0.04     -3.95      4.05    633.27      1.00\n",
      " intersection[59]     -0.14      2.29     -0.14     -3.08      4.56    541.12      1.00\n",
      " intersection[60]     -0.32      2.21     -0.10     -4.31      2.88    737.51      1.00\n",
      " intersection[61]      0.30      2.51      0.21     -3.75      4.28    492.89      1.01\n",
      " intersection[62]     -0.27      2.32     -0.15     -4.06      3.42    428.93      1.00\n",
      " intersection[63]     -0.52      2.35     -0.27     -4.68      2.96    441.23      1.00\n",
      " intersection[64]     -0.29      2.31     -0.22     -4.30      3.51    441.06      1.01\n",
      " intersection[65]      0.32      2.20      0.25     -2.99      4.26    469.96      1.00\n",
      " intersection[66]      0.05      2.33      0.08     -4.21      3.53    659.84      1.00\n",
      " intersection[67]     -0.23      2.48     -0.15     -3.78      4.45    665.51      1.00\n",
      " intersection[68]     -0.24      2.32     -0.19     -3.84      3.88    648.15      1.00\n",
      " intersection[69]      0.06      2.38     -0.04     -3.74      4.00    725.10      1.00\n",
      " intersection[70]     -0.33      2.29     -0.25     -4.35      3.35    566.31      1.00\n",
      " intersection[71]      0.01      2.42      0.02     -3.80      3.87    528.10      1.00\n",
      " intersection[72]     -0.04      2.29     -0.09     -3.45      3.55    464.87      1.00\n",
      " intersection[73]     -0.17      2.32     -0.12     -4.14      3.53    802.20      1.00\n",
      " intersection[74]     -0.51      2.36     -0.26     -4.64      2.95    416.56      1.02\n",
      " intersection[75]      0.46      2.28      0.27     -3.07      4.44    610.63      1.01\n",
      " intersection[76]     -0.10      2.52     -0.13     -4.00      4.41    480.76      1.00\n",
      " intersection[77]      0.93      2.42      0.68     -2.64      5.28    360.25      1.03\n",
      " intersection[78]     -0.13      2.33     -0.08     -4.20      3.61    734.97      1.00\n",
      " intersection[79]      0.27      2.37      0.20     -3.71      3.84    566.50      1.01\n",
      " intersection[80]     -0.05      2.36     -0.03     -3.36      3.99    681.59      1.00\n",
      " intersection[81]      0.34      2.29      0.32     -3.49      3.93    800.74      1.01\n",
      " intersection[82]      0.52      2.19      0.48     -2.76      4.14    855.65      1.00\n",
      " intersection[83]     -0.09      2.26     -0.05     -3.79      3.50    783.84      1.00\n",
      " intersection[84]     -0.64      2.51     -0.39     -4.43      3.23    405.36      1.03\n",
      " intersection[85]     -0.07      2.44     -0.04     -3.96      4.11    766.34      1.00\n",
      " intersection[86]      0.13      2.31      0.06     -3.77      3.93    520.03      1.00\n",
      " intersection[87]     -0.18      2.20     -0.08     -3.73      3.44    719.20      1.00\n",
      " intersection[88]      0.02      2.16     -0.01     -3.52      3.76    509.40      1.00\n",
      " intersection[89]      0.05      2.36      0.05     -4.24      3.95    647.74      1.00\n",
      " intersection[90]     -0.14      2.33     -0.02     -3.98      3.82    673.88      1.00\n",
      " intersection[91]     -0.01      2.33     -0.01     -3.41      4.39    537.01      1.00\n",
      " intersection[92]      0.30      2.38      0.23     -4.06      3.86    596.10      1.01\n",
      " intersection[93]     -0.16      2.23     -0.18     -3.66      3.60    578.84      1.00\n",
      " intersection[94]      0.26      2.25      0.13     -3.40      3.91    704.93      1.00\n",
      " intersection[95]      0.25      2.21      0.18     -3.38      4.06    681.73      1.00\n",
      " intersection[96]     -0.07      2.18     -0.09     -3.78      3.42    693.63      1.00\n",
      " intersection[97]      0.05      2.31      0.04     -3.25      4.78    635.96      1.00\n",
      " intersection[98]      0.05      2.13      0.08     -3.28      3.61    762.25      1.00\n",
      " intersection[99]     -0.06      2.31     -0.09     -3.93      3.56    597.44      1.00\n",
      "intersection[100]     -0.09      2.34     -0.06     -3.55      4.14    453.09      1.00\n",
      "intersection[101]      0.25      2.47      0.14     -3.61      4.46    630.57      1.00\n",
      "intersection[102]      0.14      2.25      0.01     -3.41      4.04    865.13      1.00\n",
      "intersection[103]      0.59      2.49      0.42     -3.05      4.81    432.16      1.01\n",
      "intersection[104]      0.03      2.36      0.08     -4.09      3.64    731.59      1.00\n",
      "intersection[105]      0.15      2.36      0.09     -3.45      4.56    537.11      1.00\n",
      "intersection[106]      0.06      2.27     -0.06     -4.07      3.44    538.32      1.00\n",
      "intersection[107]      0.50      2.35      0.39     -3.14      4.17    511.99      1.01\n",
      "intersection[108]      0.22      2.29      0.22     -3.01      4.66    762.83      1.00\n",
      "intersection[109]      0.12      2.19      0.15     -3.18      3.62    450.30      1.00\n",
      "intersection[110]     -0.03      2.46      0.08     -4.61      3.62    647.44      1.00\n",
      "intersection[111]     -0.11      2.25     -0.06     -3.75      3.55    583.93      1.00\n",
      "intersection[112]     -0.30      2.27     -0.22     -4.24      3.03    494.58      1.00\n",
      "intersection[113]     -0.19      2.34     -0.10     -4.85      3.22    588.92      1.00\n",
      "intersection[114]     -0.02      2.42     -0.09     -4.15      3.76    479.99      1.00\n",
      "intersection[115]      0.29      2.33      0.20     -3.67      3.79    672.86      1.00\n",
      "intersection[116]      0.44      2.33      0.35     -3.39      4.25    675.38      1.01\n",
      "intersection[117]     -0.13      2.34     -0.16     -4.40      3.19    529.41      1.00\n",
      "intersection[118]     -0.33      2.29     -0.23     -3.95      3.66    503.23      1.00\n",
      "intersection[119]     -0.10      2.42     -0.02     -4.14      3.71    556.55      1.00\n",
      "intersection[120]     -0.32      2.19     -0.21     -4.28      3.01    627.35      1.01\n",
      "intersection[121]     -0.05      2.45     -0.09     -4.17      3.65    618.17      1.00\n",
      "intersection[122]     -0.40      2.43     -0.30     -3.99      3.83    728.35      1.01\n",
      "intersection[123]     -0.43      2.23     -0.24     -4.40      3.15    443.55      1.01\n",
      "intersection[124]      0.16      2.46      0.09     -3.73      4.59    437.76      1.01\n",
      "intersection[125]      0.04      2.33     -0.01     -3.41      4.17    685.48      1.00\n",
      "intersection[126]     -0.40      2.23     -0.28     -4.68      2.82    669.73      1.00\n",
      "intersection[127]     -0.15      2.44     -0.09     -3.89      4.01    566.92      1.00\n",
      "intersection[128]      0.20      2.34      0.14     -3.66      3.96    549.11      1.01\n",
      "intersection[129]      0.09      2.22      0.10     -3.59      3.46    427.82      1.00\n",
      "intersection[130]     -0.18      2.43     -0.04     -3.78      3.60    540.66      1.00\n",
      "intersection[131]     -0.05      2.34      0.02     -3.60      3.87    637.97      1.00\n",
      "intersection[132]     -0.05      2.19     -0.04     -3.09      4.24    743.42      1.00\n",
      "intersection[133]     -0.33      2.37     -0.23     -4.45      3.34    579.13      1.00\n",
      "intersection[134]      0.07      2.27      0.08     -3.61      3.56    685.18      1.00\n",
      "intersection[135]      0.52      2.36      0.33     -3.01      4.65    398.90      1.00\n",
      "intersection[136]      0.25      2.38      0.09     -3.51      4.49    450.13      1.00\n",
      "intersection[137]     -0.31      2.23     -0.30     -4.08      3.28    695.34      1.00\n",
      "intersection[138]     -0.27      2.34     -0.22     -3.93      3.78    664.79      1.00\n",
      "intersection[139]      0.08      2.42      0.04     -4.19      4.11    620.66      1.00\n",
      "intersection[140]      0.42      2.33      0.28     -3.90      3.68    703.82      1.01\n",
      "intersection[141]     -0.20      2.22     -0.08     -3.97      3.38    741.19      1.00\n",
      "intersection[142]     -0.02      2.19     -0.01     -3.32      3.89    607.78      1.00\n",
      "intersection[143]     -0.05      2.36     -0.02     -3.99      3.71    490.09      1.00\n",
      "intersection[144]      0.40      2.23      0.28     -3.08      4.16    551.49      1.00\n",
      "intersection[145]     -0.03      2.57     -0.04     -3.97      4.04    334.15      1.00\n",
      "intersection[146]      0.05      2.28      0.13     -4.19      3.36    494.97      1.00\n",
      "intersection[147]      0.51      2.36      0.41     -3.18      3.95    583.38      1.01\n",
      "intersection[148]     -0.04      2.37      0.05     -3.73      3.91    741.27      1.00\n",
      "intersection[149]      0.07      2.35      0.07     -3.84      3.86    563.27      1.00\n",
      "intersection[150]     -0.05      2.33      0.04     -4.01      3.72    394.25      1.00\n",
      "intersection[151]      0.44      2.16      0.33     -2.89      4.21    709.00      1.00\n",
      "intersection[152]      0.20      2.34      0.19     -4.01      3.35    550.23      1.00\n",
      "intersection[153]     -0.05      2.31     -0.07     -3.77      3.56    594.91      1.00\n",
      "intersection[154]      0.34      2.34      0.23     -3.16      4.47    499.75      1.00\n",
      "intersection[155]      0.02      2.43      0.01     -4.29      3.55    538.40      1.00\n",
      "intersection[156]      0.05      2.35      0.02     -3.91      3.65    768.68      1.00\n",
      "intersection[157]      0.16      2.35      0.11     -3.59      4.40    680.69      1.00\n",
      "intersection[158]      0.34      2.17      0.23     -3.40      3.83    526.09      1.01\n",
      "intersection[159]      0.25      2.31      0.23     -3.41      3.88    549.30      1.01\n",
      "intersection[160]      0.32      2.29      0.22     -4.33      3.52    947.54      1.01\n",
      "intersection[161]     -0.28      2.33     -0.29     -4.00      3.58    591.22      1.00\n",
      "intersection[162]      0.09      2.30      0.03     -3.75      3.57    583.82      1.00\n",
      "intersection[163]      0.15      2.44      0.11     -3.90      4.07    575.86      1.00\n",
      "intersection[164]     -0.12      2.42     -0.16     -3.88      3.96    655.43      1.00\n",
      "intersection[165]     -0.17      2.16     -0.12     -3.40      3.59    599.77      1.00\n",
      "intersection[166]     -0.01      2.39     -0.02     -3.52      4.53    429.19      1.00\n",
      "intersection[167]      0.06      2.37     -0.01     -3.88      4.16    720.31      1.00\n",
      "intersection[168]     -0.09      2.58     -0.04     -4.41      3.77    439.23      1.00\n",
      "intersection[169]      0.15      2.19      0.08     -3.29      3.89    653.87      1.00\n",
      "intersection[170]      0.18      2.41      0.08     -4.49      3.79    626.74      1.00\n",
      "intersection[171]      0.08      2.32      0.07     -3.62      3.72    524.27      1.00\n",
      "intersection[172]      0.02      2.47      0.06     -3.94      3.86    754.25      1.00\n",
      "intersection[173]     -0.16      2.27     -0.12     -3.91      3.47    760.70      1.00\n",
      "intersection[174]     -0.10      2.20     -0.14     -3.57      3.71    588.20      1.00\n",
      "intersection[175]      0.14      2.37      0.11     -3.75      4.36    498.15      1.00\n",
      "intersection[176]     -0.28      2.29     -0.11     -3.81      3.57    565.09      1.00\n",
      "intersection[177]     -0.12      2.32     -0.07     -3.86      3.70    593.35      1.00\n",
      "intersection[178]      0.56      2.38      0.36     -3.17      4.53    328.17      1.01\n",
      "intersection[179]      0.17      2.24      0.22     -3.19      4.25    677.25      1.00\n",
      "intersection[180]     -0.13      2.38     -0.02     -3.86      4.02    516.15      1.00\n",
      "intersection[181]     -0.18      2.35     -0.09     -3.85      4.08    609.25      1.00\n",
      "intersection[182]     -0.15      2.34     -0.08     -4.34      3.49    581.82      1.00\n",
      "intersection[183]     -0.24      2.24     -0.12     -4.01      3.13    779.88      1.01\n",
      "intersection[184]      0.10      2.39      0.05     -3.93      4.21    680.33      1.00\n",
      "intersection[185]     -0.06      2.24      0.00     -3.73      3.71    703.60      1.00\n",
      "intersection[186]     -0.33      2.38     -0.14     -4.52      3.64    376.48      1.01\n",
      "intersection[187]     -0.07      2.28     -0.07     -4.19      3.38    657.78      1.00\n",
      "intersection[188]      0.26      2.29      0.23     -3.42      3.97    586.66      1.00\n",
      "intersection[189]      0.39      2.44      0.28     -3.34      4.91    615.14      1.00\n",
      "intersection[190]      0.21      2.24      0.13     -3.48      3.70    797.03      1.00\n",
      "intersection[191]      0.25      2.27      0.18     -3.36      3.98    715.28      1.00\n",
      "intersection[192]     -0.08      2.39     -0.10     -3.95      3.89    615.98      1.00\n",
      "intersection[193]      0.19      2.18      0.13     -3.23      3.66    682.91      1.00\n",
      "intersection[194]     -0.35      2.16     -0.25     -3.73      3.40    554.03      1.00\n",
      "intersection[195]     -0.10      2.54     -0.12     -4.97      3.54    579.73      1.00\n",
      "intersection[196]     -0.17      2.42     -0.15     -4.48      3.29    423.57      1.01\n",
      "intersection[197]     -0.43      2.40     -0.27     -4.17      3.69    497.36      1.01\n",
      "intersection[198]      0.18      2.22      0.14     -3.52      3.62    475.42      1.00\n",
      "intersection[199]     -0.58      2.33     -0.30     -4.71      3.20    262.85      1.02\n",
      "intersection[200]      0.34      2.16      0.23     -2.70      4.33    474.10      1.00\n",
      "intersection[201]      0.06      2.23     -0.01     -3.59      3.73    690.85      1.00\n",
      "intersection[202]      0.07      2.48     -0.03     -3.99      3.92    467.00      1.01\n",
      "intersection[203]     -0.05      2.33     -0.04     -4.42      3.36    633.62      1.00\n",
      "intersection[204]     -0.00      2.27      0.11     -3.48      3.53    685.50      1.00\n",
      "intersection[205]      0.14      2.33      0.10     -3.14      4.23    659.21      1.00\n",
      "intersection[206]      0.20      2.34      0.20     -3.91      3.67    667.80      1.00\n",
      "intersection[207]     -0.09      2.24     -0.10     -3.33      3.88    606.87      1.00\n",
      "intersection[208]      0.38      2.62      0.31     -2.90      5.48    470.50      1.00\n",
      "intersection[209]     -0.05      2.62      0.00     -4.73      4.45    467.47      1.00\n",
      "intersection[210]     -0.21      2.11     -0.10     -3.46      3.52    515.80      1.00\n",
      "intersection[211]      0.14      2.41      0.07     -4.10      4.06    631.21      1.00\n",
      "intersection[212]     -0.30      2.27     -0.10     -4.12      2.99    621.63      1.00\n",
      "intersection[213]     -0.31      2.31     -0.26     -4.31      3.18    397.31      1.02\n",
      "intersection[214]      0.30      2.30      0.27     -3.24      4.45    470.65      1.00\n",
      "intersection[215]      0.12      2.08      0.10     -3.63      3.33    573.21      1.00\n",
      "intersection[216]     -0.16      2.30     -0.13     -3.52      4.23    718.65      1.00\n",
      "intersection[217]      0.12      2.46      0.23     -3.93      4.17    616.21      1.00\n",
      "intersection[218]     -0.15      2.29     -0.06     -4.28      3.22    675.48      1.00\n",
      "intersection[219]      0.33      2.32      0.18     -3.49      4.02    639.85      1.00\n",
      "intersection[220]      0.12      2.49      0.16     -4.39      3.63    611.82      1.00\n",
      "intersection[221]     -0.20      2.30     -0.10     -4.03      3.72    378.71      1.01\n",
      "intersection[222]     -0.38      2.22     -0.17     -3.61      3.64    553.05      1.01\n",
      "intersection[223]     -0.05      2.32      0.03     -3.80      3.63    626.97      1.00\n",
      "intersection[224]     -0.62      2.50     -0.37     -4.48      3.66    509.75      1.01\n",
      "intersection[225]     -0.25      2.37     -0.19     -4.11      3.65    474.39      1.00\n",
      "intersection[226]      0.29      2.19      0.28     -3.50      3.71    739.35      1.00\n",
      "intersection[227]     -0.21      2.26     -0.14     -4.02      3.38    612.57      1.00\n",
      "intersection[228]      0.10      2.24      0.05     -3.30      4.14    541.45      1.00\n",
      "intersection[229]      0.46      2.23      0.38     -3.04      4.09    442.94      1.00\n",
      "intersection[230]     -0.12      2.29     -0.07     -3.56      4.05    617.69      1.00\n",
      "intersection[231]     -0.39      2.67     -0.17     -5.39      3.63    394.42      1.01\n",
      "intersection[232]     -0.48      2.27     -0.29     -4.35      2.86    512.80      1.02\n",
      "intersection[233]     -0.12      2.23     -0.16     -4.13      3.45    703.90      1.00\n",
      "intersection[234]      0.07      2.27      0.06     -3.94      3.61    741.54      1.00\n",
      "intersection[235]     -0.03      2.27     -0.01     -3.56      4.23    730.25      1.00\n",
      "intersection[236]      0.03      2.14      0.01     -3.33      3.68    888.90      1.00\n",
      "intersection[237]     -0.31      2.55     -0.20     -4.47      4.31    449.64      1.02\n",
      "intersection[238]      0.12      2.34      0.03     -3.10      4.78    758.97      1.00\n",
      "intersection[239]     -0.22      2.44     -0.19     -4.04      3.67    781.99      1.00\n",
      "intersection[240]     -0.29      2.31     -0.18     -3.89      3.92    431.98      1.01\n",
      "intersection[241]     -0.07      2.17     -0.01     -3.61      3.44    623.79      1.00\n",
      "intersection[242]      0.07      2.42      0.02     -3.26      4.41    635.89      1.00\n",
      "intersection[243]     -0.45      2.49     -0.28     -4.60      3.06    504.56      1.01\n",
      "intersection[244]     -0.61      2.32     -0.37     -4.44      3.16    442.17      1.02\n",
      "intersection[245]     -0.18      2.23     -0.13     -3.76      3.54    656.61      1.00\n",
      "intersection[246]      0.03      2.44      0.08     -3.84      3.92    629.34      1.00\n",
      "intersection[247]     -0.22      2.56     -0.09     -5.20      3.52    651.60      1.00\n",
      "intersection[248]      0.11      2.51      0.07     -3.98      4.09    497.23      1.00\n",
      "intersection[249]      0.09      2.36     -0.01     -3.92      3.78    593.36      1.00\n",
      "intersection[250]     -0.41      2.34     -0.40     -3.61      4.17    420.88      1.00\n",
      "intersection[251]      0.03      2.30     -0.02     -3.91      3.84    386.36      1.00\n",
      "intersection[252]      0.08      2.34      0.04     -4.35      3.35    691.30      1.00\n",
      "intersection[253]     -0.32      2.35     -0.29     -4.16      3.51    677.09      1.00\n",
      "intersection[254]      0.07      2.36     -0.03     -3.32      4.34    563.78      1.00\n",
      "intersection[255]      0.49      2.31      0.34     -3.27      4.16    560.95      1.01\n",
      "intersection[256]     -0.54      2.30     -0.30     -4.10      3.24    461.08      1.02\n",
      "intersection[257]      0.23      2.27      0.20     -3.61      4.01    468.61      1.01\n",
      "intersection[258]      0.41      2.36      0.37     -3.61      4.41    427.37      1.01\n",
      "intersection[259]     -0.29      2.43     -0.24     -4.11      3.68    718.17      1.00\n",
      "intersection[260]      0.04      2.34      0.13     -3.99      3.39    650.62      1.00\n",
      "intersection[261]      0.16      2.43      0.19     -4.12      3.84    733.21      1.00\n",
      "intersection[262]     -0.41      2.42     -0.28     -4.18      3.74    613.81      1.01\n",
      "intersection[263]     -0.22      2.23     -0.16     -3.93      3.35    651.67      1.00\n",
      "intersection[264]     -0.33      2.13     -0.25     -4.16      2.81    445.80      1.01\n",
      "intersection[265]      0.20      2.18      0.13     -3.45      3.91    591.77      1.00\n",
      "intersection[266]      0.02      2.37     -0.03     -3.98      4.02    457.74      1.00\n",
      "intersection[267]     -0.05      2.55     -0.05     -4.26      3.99    550.49      1.00\n",
      "intersection[268]      0.35      2.13      0.21     -2.81      4.29    511.61      1.00\n",
      "intersection[269]     -0.24      2.34     -0.17     -4.56      3.27    752.32      1.00\n",
      "intersection[270]     -0.05      2.37      0.03     -3.85      3.78    638.53      1.00\n",
      "intersection[271]      0.04      2.21      0.06     -3.51      3.82    661.22      1.00\n",
      "intersection[272]     -0.14      2.27     -0.09     -3.97      3.52    647.79      1.01\n",
      "intersection[273]      0.32      2.56      0.20     -3.65      4.93    422.70      1.01\n",
      "intersection[274]     -0.43      2.38     -0.22     -4.14      3.85    787.06      1.01\n",
      "intersection[275]      0.17      2.11      0.12     -3.30      3.76    482.67      1.00\n",
      "intersection[276]      0.24      2.35      0.18     -3.25      4.35    669.52      1.00\n",
      "intersection[277]      0.06      2.53      0.04     -4.04      4.36    540.85      1.00\n",
      "intersection[278]     -0.19      2.53     -0.10     -4.78      3.37    634.96      1.00\n",
      "intersection[279]      0.01      2.28      0.05     -3.46      3.96    560.73      1.00\n",
      "intersection[280]      0.33      2.23      0.20     -3.43      3.73    748.19      1.00\n",
      "intersection[281]     -0.29      2.36     -0.20     -4.08      3.83    577.23      1.00\n",
      "intersection[282]     -0.35      2.38     -0.24     -4.34      3.44    364.31      1.00\n",
      "intersection[283]      0.03      2.26      0.06     -3.64      3.50    744.86      1.00\n",
      "intersection[284]     -0.01      2.35     -0.01     -3.86      4.11    853.33      1.00\n",
      "intersection[285]      0.75      2.56      0.64     -3.17      5.07    590.34      1.00\n",
      "intersection[286]     -0.00      2.46      0.05     -4.28      4.10    517.18      1.00\n",
      "intersection[287]      0.42      2.23      0.35     -3.06      3.97    691.88      1.01\n",
      "intersection[288]     -0.45      2.45     -0.20     -4.02      4.23    483.94      1.02\n",
      "intersection[289]      0.35      2.29      0.22     -3.03      4.56    683.95      1.01\n",
      "intersection[290]      0.31      2.29      0.20     -3.23      4.04    388.08      1.01\n",
      "intersection[291]      0.38      2.27      0.17     -3.80      3.98    373.75      1.02\n",
      "intersection[292]     -0.05      2.23      0.00     -3.81      3.58    749.64      1.00\n",
      "intersection[293]     -0.18      2.41     -0.19     -4.17      3.68    517.79      1.00\n",
      "intersection[294]     -0.37      2.26     -0.20     -3.84      3.37    664.28      1.02\n",
      "intersection[295]     -0.03      2.25      0.05     -3.89      3.51    579.48      1.00\n",
      "intersection[296]      0.04      2.30     -0.00     -3.66      4.06    577.74      1.00\n",
      "intersection[297]     -0.40      2.50     -0.20     -4.39      3.76    384.57      1.01\n",
      "intersection[298]      0.53      2.28      0.39     -3.05      4.37    601.23      1.01\n",
      "intersection[299]      0.38      2.28      0.22     -3.18      4.14    728.92      1.00\n",
      "intersection[300]      0.95      2.30      0.71     -2.61      4.76    190.24      1.03\n",
      "intersection[301]     -0.15      2.45     -0.07     -4.30      3.77    661.11      1.00\n",
      "intersection[302]     -0.09      2.30      0.02     -3.93      3.73    654.53      1.00\n",
      "intersection[303]     -0.57      2.36     -0.37     -4.01      3.38    623.22      1.01\n",
      "intersection[304]     -0.02      2.12     -0.10     -3.57      3.36    549.18      1.00\n",
      "intersection[305]     -0.11      2.38     -0.01     -3.95      4.01    696.45      1.00\n",
      "intersection[306]      0.13      2.49      0.05     -3.79      4.43    789.95      1.00\n",
      "intersection[307]     -0.07      2.39      0.01     -3.44      4.25    633.70      1.00\n",
      "intersection[308]      0.11      2.44      0.08     -4.12      3.96    572.38      1.00\n",
      "intersection[309]     -0.40      2.22     -0.28     -4.19      3.14    548.75      1.00\n",
      "intersection[310]     -0.16      2.16     -0.06     -3.80      3.24    709.08      1.00\n",
      "intersection[311]     -0.14      2.31     -0.08     -4.15      3.65    526.65      1.00\n",
      "intersection[312]      0.25      2.22      0.20     -3.32      3.67    757.21      1.00\n",
      "intersection[313]     -0.02      2.09      0.05     -3.57      3.33    661.97      1.00\n",
      "intersection[314]      0.06      2.31      0.08     -3.62      3.97   1030.09      1.00\n",
      "intersection[315]      0.18      2.28      0.06     -2.85      4.72    610.97      1.00\n",
      "intersection[316]     -0.25      2.28     -0.20     -4.32      3.03    616.16      1.00\n",
      "intersection[317]     -0.30      2.33     -0.19     -4.06      3.43    586.64      1.00\n",
      "intersection[318]      0.39      2.17      0.25     -3.42      3.82    555.36      1.00\n",
      "intersection[319]     -0.36      2.21     -0.31     -4.58      2.90    428.76      1.01\n",
      "intersection[320]     -0.04      2.42      0.04     -3.59      4.47    517.62      1.00\n",
      "intersection[321]      0.11      2.37      0.10     -3.69      4.17    707.17      1.00\n",
      "intersection[322]      0.08      2.59      0.12     -3.75      4.40    382.73      1.00\n",
      "intersection[323]      0.11      2.41      0.02     -4.06      3.47    604.24      1.00\n",
      "intersection[324]     -0.36      2.44     -0.31     -3.75      4.49    635.78      1.00\n",
      "intersection[325]     -0.19      2.16     -0.21     -3.41      3.73    677.46      1.00\n",
      "intersection[326]     -0.22      2.25     -0.08     -4.35      3.10    709.28      1.00\n",
      "intersection[327]     -0.30      2.32     -0.12     -4.14      3.51    560.02      1.01\n",
      "intersection[328]     -0.01      2.33     -0.02     -4.13      3.47    432.21      1.00\n",
      "intersection[329]      0.10      2.24      0.05     -3.32      4.08    712.74      1.00\n",
      "intersection[330]     -0.53      2.35     -0.31     -4.78      2.90    372.12      1.02\n",
      "intersection[331]      0.09      2.18     -0.03     -3.64      3.42    492.01      1.00\n",
      "intersection[332]      0.29      2.40      0.15     -3.40      4.35    793.76      1.01\n",
      "intersection[333]     -0.48      2.27     -0.22     -4.18      3.29    333.05      1.01\n",
      "intersection[334]     -0.23      2.44     -0.12     -4.21      3.63    333.53      1.01\n",
      "intersection[335]      0.07      2.34      0.04     -4.23      3.79    638.48      1.00\n",
      "intersection[336]     -0.39      2.37     -0.26     -4.40      3.42    701.18      1.01\n",
      "intersection[337]     -0.22      2.37     -0.10     -4.17      3.59    556.28      1.01\n",
      "intersection[338]      0.50      2.27      0.42     -2.92      4.39    397.38      1.01\n",
      "intersection[339]      0.47      2.29      0.34     -3.21      4.23    571.51      1.01\n",
      "intersection[340]      0.20      2.34      0.17     -3.08      4.73    578.79      1.00\n",
      "intersection[341]     -0.35      2.27     -0.22     -4.02      3.28    754.12      1.01\n",
      "intersection[342]     -0.49      2.23     -0.32     -4.11      3.17    440.48      1.01\n",
      "intersection[343]      0.28      2.25      0.15     -3.35      4.17    622.43      1.00\n",
      "intersection[344]      0.06      2.22      0.06     -3.54      3.40    805.17      1.00\n",
      "intersection[345]      0.10      2.31      0.05     -3.30      4.21    512.16      1.00\n",
      "intersection[346]     -0.13      2.29     -0.06     -3.46      4.03    643.38      1.00\n",
      "intersection[347]     -0.20      2.26     -0.08     -4.27      3.23    351.79      1.00\n",
      "intersection[348]      0.46      2.16      0.36     -3.34      3.67    558.47      1.00\n",
      "intersection[349]      0.07      2.30      0.09     -4.01      3.43    485.10      1.00\n",
      "intersection[350]     -0.22      2.32     -0.11     -3.95      3.40    777.66      1.00\n",
      "intersection[351]     -0.42      2.44     -0.26     -4.46      3.78    736.96      1.01\n",
      "intersection[352]      0.06      2.23      0.09     -3.80      3.77    724.13      1.00\n",
      "intersection[353]     -0.08      2.40     -0.01     -3.87      4.03    702.01      1.00\n",
      "intersection[354]      0.22      2.35      0.20     -3.86      3.87    551.26      1.00\n",
      "intersection[355]      0.19      2.21      0.15     -3.28      3.71    546.20      1.00\n",
      "intersection[356]      0.05      2.26      0.06     -3.12      4.33    481.03      1.00\n",
      "intersection[357]      0.24      2.21      0.20     -3.19      3.76    809.07      1.00\n",
      "intersection[358]      0.40      2.38      0.32     -3.79      3.83    369.28      1.01\n",
      "intersection[359]     -0.03      2.39      0.01     -3.90      3.85    562.48      1.01\n",
      "intersection[360]      0.39      2.41      0.19     -3.07      4.33    455.85      1.00\n",
      "intersection[361]      0.31      2.37      0.24     -3.49      4.11    556.32      1.00\n",
      "intersection[362]      0.37      2.32      0.20     -3.63      4.20    494.84      1.00\n",
      "intersection[363]      0.41      2.38      0.24     -3.47      4.16    663.30      1.00\n",
      "intersection[364]     -0.10      2.49     -0.07     -4.19      4.07    477.66      1.00\n",
      "intersection[365]      0.13      2.32      0.07     -3.59      3.72    724.73      1.00\n",
      "intersection[366]      0.53      2.53      0.36     -4.02      4.29    330.56      1.01\n",
      "intersection[367]     -0.44      2.37     -0.33     -4.29      3.05    692.04      1.00\n",
      "intersection[368]      0.20      2.28      0.15     -3.83      3.55    641.20      1.00\n",
      "intersection[369]     -0.40      2.40     -0.18     -4.24      3.58    586.51      1.00\n",
      "intersection[370]     -0.13      2.27     -0.09     -3.37      3.81    488.69      1.00\n",
      "intersection[371]     -0.20      2.23     -0.18     -4.19      3.26    509.13      1.00\n",
      "intersection[372]     -0.10      2.56     -0.11     -4.08      4.53    523.73      1.00\n",
      "intersection[373]      0.23      2.33      0.12     -3.80      4.05    563.39      1.00\n",
      "intersection[374]      0.37      2.42      0.24     -3.65      4.14    428.96      1.02\n",
      "intersection[375]      0.76      2.27      0.56     -2.92      4.54    781.20      1.01\n",
      "intersection[376]     -0.52      2.21     -0.34     -4.45      2.85    515.25      1.01\n",
      "intersection[377]     -0.14      2.51     -0.12     -4.07      4.11    552.84      1.00\n",
      "intersection[378]      0.40      2.26      0.26     -3.46      3.82    512.84      1.01\n",
      "intersection[379]      0.42      2.06      0.26     -2.99      3.76    599.40      1.00\n",
      "intersection[380]      0.16      2.28      0.07     -3.82      3.52    699.18      1.01\n",
      "intersection[381]      0.48      2.27      0.30     -2.94      4.47    507.97      1.00\n",
      "intersection[382]     -0.34      2.26     -0.28     -4.10      3.47    550.12      1.00\n",
      "intersection[383]      0.11      2.34      0.09     -4.69      3.13    512.14      1.00\n",
      "intersection[384]      0.03      2.33     -0.02     -4.04      3.43    663.25      1.00\n",
      "intersection[385]     -0.09      2.45     -0.08     -3.96      3.92    619.42      1.00\n",
      "intersection[386]     -0.08      2.52     -0.11     -3.97      4.17    679.22      1.00\n",
      "intersection[387]     -0.19      2.12     -0.17     -3.26      3.39    769.56      1.00\n",
      "intersection[388]      0.16      2.28      0.18     -3.95      3.53    610.84      1.00\n",
      "intersection[389]     -0.10      2.32     -0.13     -3.86      3.71    650.46      1.00\n",
      "intersection[390]     -0.21      2.32     -0.18     -3.94      3.44    457.02      1.01\n",
      "intersection[391]     -0.28      2.40     -0.24     -4.61      3.59    538.40      1.00\n",
      "intersection[392]     -0.02      2.13      0.02     -3.34      3.28    586.13      1.00\n",
      "intersection[393]     -0.15      2.61     -0.07     -4.32      4.15    772.71      1.00\n",
      "intersection[394]      0.01      2.28     -0.07     -3.89      3.79    651.84      1.00\n",
      "intersection[395]      0.35      2.41      0.19     -3.53      4.44    552.73      1.02\n",
      "intersection[396]     -0.66      2.39     -0.37     -4.92      2.68    512.50      1.02\n",
      "intersection[397]     -0.04      2.26     -0.06     -3.86      3.50    442.65      1.00\n",
      "intersection[398]     -0.07      2.29     -0.06     -3.82      3.69    676.24      1.00\n",
      "intersection[399]      0.06      2.45      0.09     -4.26      3.91    594.16      1.00\n",
      "intersection[400]      0.07      2.34      0.10     -3.88      3.92    548.74      1.00\n",
      "intersection[401]      0.06      2.46      0.15     -4.26      4.22    423.16      1.00\n",
      "intersection[402]      0.16      2.19      0.08     -3.78      3.61    493.82      1.00\n",
      "intersection[403]     -0.44      2.25     -0.24     -4.26      2.77    725.29      1.01\n",
      "intersection[404]     -0.08      2.27     -0.03     -4.18      3.14    586.40      1.00\n",
      "intersection[405]      0.25      2.54      0.02     -3.76      4.55    513.94      1.00\n",
      "intersection[406]     -0.06      2.36     -0.06     -3.21      4.61    739.62      1.00\n",
      "intersection[407]     -0.16      2.42     -0.12     -3.65      4.13    584.60      1.00\n",
      "intersection[408]     -0.28      2.32     -0.24     -4.43      3.20    663.54      1.01\n",
      "intersection[409]     -0.16      2.24     -0.08     -4.11      3.48    494.24      1.00\n",
      "intersection[410]     -0.16      2.31     -0.05     -3.76      3.73    779.98      1.00\n",
      "intersection[411]      0.28      2.26      0.13     -3.50      4.03    486.71      1.01\n",
      "intersection[412]     -0.04      2.31     -0.04     -3.69      3.58    510.41      1.00\n",
      "intersection[413]     -0.38      2.34     -0.22     -4.31      3.19    656.35      1.00\n",
      "intersection[414]     -0.17      2.19     -0.06     -3.92      3.30    763.00      1.00\n",
      "intersection[415]     -0.52      2.15     -0.23     -4.63      2.42    551.22      1.01\n",
      "intersection[416]      0.14      2.35      0.12     -3.59      4.22    587.78      1.01\n",
      "intersection[417]      0.08      2.42      0.02     -3.91      4.34    743.56      1.00\n",
      "intersection[418]      0.35      2.21      0.29     -2.76      4.37    719.78      1.00\n",
      "intersection[419]      0.02      2.31      0.05     -3.65      3.88    833.85      1.00\n",
      "intersection[420]      0.18      2.26      0.06     -3.52      4.03    680.12      1.00\n",
      "intersection[421]     -0.00      2.24     -0.03     -3.25      3.97    654.50      1.00\n",
      "intersection[422]     -0.42      2.38     -0.22     -4.33      3.34    294.47      1.01\n",
      "intersection[423]      0.02      2.56     -0.03     -4.66      3.69    459.54      1.00\n",
      "intersection[424]      0.38      2.43      0.28     -3.86      4.36    491.07      1.00\n",
      "intersection[425]      0.07      2.51      0.09     -4.24      4.11    422.72      1.00\n",
      "intersection[426]      0.67      2.40      0.43     -2.63      5.03    450.28      1.02\n",
      "intersection[427]     -0.43      2.14     -0.27     -4.41      2.74    695.19      1.01\n",
      "intersection[428]      0.21      2.32      0.13     -3.45      4.35    681.45      1.00\n",
      "intersection[429]     -0.41      2.40     -0.28     -4.78      3.14    660.52      1.01\n",
      "intersection[430]     -0.24      2.33     -0.11     -4.23      3.62    423.92      1.00\n",
      "intersection[431]      0.28      2.38      0.13     -3.47      4.82    678.07      1.00\n",
      "intersection[432]     -0.89      2.34     -0.65     -5.09      2.50    141.48      1.05\n",
      "intersection[433]      0.52      2.20      0.37     -2.97      4.15    522.11      1.01\n",
      "intersection[434]     -0.09      2.29     -0.08     -4.64      3.14    492.68      1.00\n",
      "intersection[435]     -0.17      2.17     -0.09     -3.98      3.40    867.86      1.00\n",
      "intersection[436]     -0.21      2.51     -0.17     -4.41      4.00    416.34      1.00\n",
      "intersection[437]     -0.34      2.34     -0.23     -4.64      3.46    456.64      1.00\n",
      "intersection[438]      0.32      2.30      0.16     -4.04      3.79    681.84      1.00\n",
      "intersection[439]      0.35      2.28      0.27     -2.98      4.18    732.24      1.01\n",
      "intersection[440]     -0.28      2.23     -0.24     -4.62      2.89    572.17      1.00\n",
      "intersection[441]     -0.14      2.38     -0.17     -4.13      3.86    734.31      1.00\n",
      "intersection[442]      0.09      2.40      0.01     -4.27      3.47    489.91      1.00\n",
      "intersection[443]     -0.31      2.45     -0.22     -4.42      3.69    537.92      1.01\n",
      "intersection[444]     -0.10      2.27     -0.05     -4.01      3.84    577.96      1.00\n",
      "intersection[445]     -0.26      2.48     -0.14     -4.33      3.55    561.56      1.00\n",
      "intersection[446]     -0.35      2.13     -0.29     -4.03      3.07    416.00      1.01\n",
      "intersection[447]      0.10      2.41      0.16     -3.66      4.32    353.99      1.00\n",
      "intersection[448]      0.25      2.48      0.23     -3.84      4.70    542.70      1.00\n",
      "intersection[449]      0.21      2.39      0.13     -3.75      4.03    453.05      1.01\n",
      "intersection[450]      0.14      2.23      0.10     -3.56      3.83    723.69      1.00\n",
      "intersection[451]      0.52      2.36      0.23     -2.98      4.65    652.95      1.02\n",
      "intersection[452]     -0.29      2.30     -0.24     -3.77      3.62    698.12      1.00\n",
      "intersection[453]     -0.03      2.33     -0.02     -3.46      4.44    716.93      1.00\n",
      "intersection[454]      0.19      2.45      0.11     -3.01      5.21    681.56      1.01\n",
      "intersection[455]      0.46      2.22      0.34     -3.11      3.99    603.87      1.01\n",
      "intersection[456]     -0.09      2.40     -0.04     -4.47      3.55    596.35      1.00\n",
      "intersection[457]     -0.29      2.15     -0.19     -4.02      2.84    564.80      1.00\n",
      "intersection[458]      0.12      2.18      0.06     -3.38      3.54    573.96      1.00\n",
      "intersection[459]      0.16      2.48      0.10     -3.27      4.36    535.61      1.00\n",
      "intersection[460]      0.47      2.24      0.36     -3.15      4.42    596.55      1.01\n",
      "intersection[461]      0.41      2.30      0.35     -3.10      4.44    656.84      1.00\n",
      "intersection[462]     -0.28      2.15     -0.18     -3.54      3.31    660.99      1.00\n",
      "intersection[463]      0.08      2.47      0.05     -4.51      3.82    520.30      1.00\n",
      "intersection[464]      0.82      2.30      0.58     -3.44      4.43    434.35      1.02\n",
      "intersection[465]     -0.01      2.25      0.07     -3.81      3.69    678.78      1.00\n",
      "intersection[466]     -0.18      2.29     -0.09     -4.29      3.64    614.63      1.00\n",
      "intersection[467]     -0.05      2.35     -0.01     -3.68      3.70    470.41      1.00\n",
      "intersection[468]      0.05      2.31     -0.06     -3.75      3.79    611.50      1.01\n",
      "intersection[469]      0.39      2.41      0.18     -3.14      4.68    533.04      1.01\n",
      "intersection[470]      0.09      2.47      0.05     -4.29      3.41    580.42      1.00\n",
      "intersection[471]     -0.11      2.39     -0.08     -4.79      3.40    643.34      1.00\n",
      "intersection[472]     -0.09      2.30     -0.08     -3.92      3.92    677.66      1.00\n",
      "intersection[473]      0.09      2.32      0.02     -3.84      3.82    905.30      1.00\n",
      "intersection[474]     -0.41      2.37     -0.28     -4.46      3.20    593.96      1.00\n",
      "intersection[475]      0.07      2.33      0.11     -4.36      3.82    674.37      1.00\n",
      "intersection[476]      0.13      2.27      0.02     -3.20      4.09    581.32      1.00\n",
      "intersection[477]      0.19      2.32      0.15     -4.04      3.66    446.49      1.00\n",
      "intersection[478]      0.53      2.55      0.39     -3.20      5.21    403.74      1.02\n",
      "intersection[479]     -0.24      2.19     -0.14     -3.71      3.24    598.94      1.00\n",
      "intersection[480]     -0.17      2.36     -0.08     -4.04      3.60    639.27      1.00\n",
      "intersection[481]      0.11      2.28      0.06     -3.77      3.90    619.96      1.01\n",
      "intersection[482]      0.15      2.29      0.13     -3.29      4.34    528.52      1.00\n",
      "intersection[483]     -0.28      2.30     -0.12     -4.41      3.16    388.75      1.01\n",
      "intersection[484]     -0.06      2.31      0.02     -3.98      3.69    440.90      1.01\n",
      "intersection[485]      0.43      2.32      0.25     -3.27      4.28    395.85      1.01\n",
      "intersection[486]      0.22      2.17      0.17     -2.86      4.25    774.04      1.00\n",
      "intersection[487]     -0.14      2.31     -0.05     -3.80      3.66    674.61      1.00\n",
      "intersection[488]      0.21      2.31      0.14     -3.24      4.15    648.46      1.00\n",
      "intersection[489]     -0.01      2.37     -0.07     -4.49      3.48    577.38      1.00\n",
      "intersection[490]      0.22      2.35      0.11     -4.04      3.73    606.29      1.01\n",
      "intersection[491]      0.25      2.10      0.20     -3.46      3.30    620.07      1.00\n",
      "intersection[492]     -0.30      2.31     -0.25     -4.50      3.23    614.33      1.00\n",
      "intersection[493]      0.22      2.25      0.26     -3.18      4.29    722.93      1.00\n",
      "intersection[494]      0.20      2.24      0.18     -3.81      3.63    636.45      1.00\n",
      "intersection[495]     -0.15      2.34     -0.10     -3.85      3.45    646.23      1.00\n",
      "intersection[496]      0.32      2.27      0.18     -3.44      3.96    579.48      1.00\n",
      "intersection[497]     -0.10      2.25     -0.04     -3.72      3.68    648.26      1.00\n",
      "intersection[498]     -0.17      2.24     -0.13     -3.75      3.33    691.64      1.00\n",
      "intersection[499]      0.08      2.38      0.02     -3.56      4.23    641.41      1.00\n",
      "              l_0      6.10     10.78      2.74      0.98     11.57    318.60      1.01\n",
      "              l_p      2.53      6.10      1.01      0.09      4.93    439.80      1.00\n",
      "              l_t      3.59     11.83      1.40      0.07      6.21    735.25      1.00\n",
      "             l_tx      1.44      0.32      1.49      0.82      1.88      4.15      1.85\n",
      "              l_x      1.03      0.07      1.02      0.90      1.14     36.69      1.01\n",
      "       propensity      0.36      0.50      0.26     -0.27      1.31    709.98      1.00\n",
      "        treatment     -0.01      1.38      0.00     -2.56      2.00    520.45      1.01\n",
      "\n",
      "Number of divergences: 184\n"
     ]
    }
   ],
   "source": [
    "# RBF Features\n",
    "gamma_p = 1 / 10**2\n",
    "gamma_t = 1 / 100**2\n",
    "Xrbfp = Nystroem(gamma=gamma_p, n_components=500).fit_transform(X)\n",
    "Xrbft = Nystroem(gamma=gamma_t, n_components=500).fit_transform(X)\n",
    "\n",
    "# Run the sampler\n",
    "rng_key = random.PRNGKey(0)\n",
    "model_mcmc.run(rng_key, Xrbfp, Xrbft, t, p, y)\n",
    "model_mcmc.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "382b564a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hierarchical approx GP Regression\n",
      "  Balanced accuracy = 0.5009 (0.0014)\n",
      "  ATE: 0.0158\n",
      "  CI (0.025, 0.975): [0.0026, 0.0304]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "gp_samples = model_mcmc.get_samples()\n",
    "w_0s = gp_samples[\"intercept\"]\n",
    "w_ps = gp_samples[\"propensity\"]\n",
    "w_ts = gp_samples[\"treatment\"]\n",
    "w_xs = gp_samples[\"confounders\"]\n",
    "w_txs = gp_samples[\"intersection\"]\n",
    "\n",
    "ate_gp_samples = np.zeros(samples)\n",
    "score_samples = np.zeros(samples)\n",
    "\n",
    "for s in range(samples):\n",
    "    pf = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], Xrbfp, Xrbft, t, p)\n",
    "    y_hat = (pf >= 0.5).astype(int)\n",
    "    pf1 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], Xrbfp, Xrbft, 1, p)\n",
    "    pf0 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], w_ps[s], Xrbfp, Xrbft, 0, p)\n",
    "    ate_gp_samples[s] = (pf1 - pf0).mean()\n",
    "    score_samples[s] = balanced_accuracy_score(y, y_hat)\n",
    "\n",
    "ate_gp = ate_gp_samples.mean()\n",
    "ci_gp = mstats.mquantiles(ate_gp_samples, prob=[0.025, 0.975])\n",
    "\n",
    "print(\"Hierarchical approx GP Regression\")\n",
    "print(f\"  Balanced accuracy = {score_samples.mean():.4f} ({score_samples.std():.4f})\")\n",
    "print(f\"  ATE: {ate_gp:.4f}\")\n",
    "print(f\"  CI (0.025, 0.975): [{ci_gp[0]:.4f}, {ci_gp[1]:.4f}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "593a11a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posteriors = [\"l_0\", \"l_x\", \"l_p\", \"l_t\", \"l_tx\"]\n",
    "for name in posteriors:\n",
    "    post = gp_samples[name]\n",
    "    plt.figure(dpi=150)\n",
    "    plt.hist(post, bins=30)\n",
    "    plt.title(name)\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "adc964a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "cnt, *_ = plt.hist(ate_gp_samples, bins=20)\n",
    "plt.plot([ate_gp, ate_gp], [0, max(cnt)], 'r', label=\"mean\")\n",
    "plt.title(\"GP approx ATE samples\")\n",
    "plt.xlabel(\"ATE\")\n",
    "plt.ylabel(\"counts\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "29",
   "metadata": {},
   "source": [
    "## Plot ATE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ate_labels = [\"GLM-Probit\", \"GLM-Logit\", \"Hierarchical-Logit\", \"Approx GP\"]\n",
    "ate = [ate_glmp, ate_glml, ate_hlr, ate_gp]\n",
    "ci = [ci_glmp, ci_glml, ci_hlr, ci_gp] \n",
    "ind = np.arange(len(ate))\n",
    "\n",
    "plt.figure(dpi=150)\n",
    "plt.vlines(ind, ymin=[c[0] for c in ci], ymax=[c[1] for c in ci], colors='k', linewidth=3)\n",
    "plt.plot(ind, ate, 'rx', markersize=10)\n",
    "plt.xticks(ind, labels=ate_labels, rotation=30)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bc6b10f0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}