Direct-Bayesian-AZ1.ipynb

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    "# Direct Regression - Bayesian Version\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",
    "   - Mental health in 2019 (**mh**). This is the transformed mental health scores from the aggregation of mental health items of the SF-36 Health Survey, as reported by the individual in 2019. It ranges from 0 to 100, with higher scores indicating better mental health.  \n",
    "   - Working hours in 2019 (**wkhr**) records the total number of hours the individual works in all jobs in a week on average. Working hours are set to 0 for those not working. \n",
    "   - Hourly Wages in 2019 (**rlwage**) records the average hourly wage for the individual’s main job in 2019. Hourly wages are set to 0 for those not working and set to missing for those reporting working more than 100 hours a week. \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)"
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "from pyro.infer import MCMC, NUTS\n",
    "\n",
    "from scipy.stats import norm, mstats\n",
    "from estimators import BayesianRidgeStat\n",
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "from sklearn.gaussian_process.kernels import WhiteKernel, Matern, DotProduct\n",
    "from sklearn.model_selection import cross_validate, KFold\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "from reed import drop_missing_treatment_or_outcome, Model, transform_outcome\n",
    "from direct_regression_SPRC import seperate_and_transform_data, print_unconditional_effects\n",
    "\n",
    "\n",
    "torch.set_default_tensor_type(torch.DoubleTensor) # set the default to float64\n",
    "%matplotlib inline\n",
    "\n",
    "# Set up a seed for numpy\n",
    "seed = 23456\n",
    "np.random.seed(seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4634",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8.2\n"
     ]
    }
   ],
   "source": [
    "print(pyro.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4635",
   "metadata": {},
   "source": [
    "## Analysis Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4636",
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "log_outcome=False\n",
    "standardize_outcome=False\n",
    "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 = 'y_wscei'\n",
    "treatment = 'redufl'\n",
    "test = False\n",
    "data_file = \"data/all_lasso_selected_100_KF_SPRC.csv\"\n",
    "xval_gp = False\n",
    "laplace_prior = False "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4637",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4638",
   "metadata": {
    "tags": [
     "hide_cell"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = data_load_func(data_file)\n",
    "drop_missing_treatment_or_outcome(data, treatment, outcome)\n",
    "data[outcome] = transform_outcome(data[outcome],log_outcome, standardize_outcome)\n",
    "\n",
    "    \n",
    "plt.hist(data[outcome])\n",
    "plt.xlabel(outcome)\n",
    "plt.ylabel(\"count\")\n",
    "plt.title(\"Distribution of outcomes\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4639",
   "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": 5,
   "id": "4640",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset has one or more *all nan* columns in : []. Separate and transform data method may fail.\n",
      "Control data dimensions:  (4043, 101)\n",
      "Treated data dimensions: (1398, 101)\n"
     ]
    }
   ],
   "source": [
    "from direct_regression_SPRC 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4641",
   "metadata": {},
   "source": [
    "## Compute unconditional/unadjusted estimate of treatment effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4642",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion Treated:26%\n",
      "Average outcome under Control:528.69±16.05\n",
      "Average outcome under Treatment:863.55±28.69\n",
      "Unadjusted treatment estimate 334.86\n"
     ]
    }
   ],
   "source": [
    "print_unconditional_effects(data, treatment, y0, y1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4643",
   "metadata": {},
   "source": [
    "## Statsmodels\n",
    "\n",
    "### OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4644",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.332\n",
      "Model:                            OLS   Adj. R-squared:                  0.320\n",
      "Method:                 Least Squares   F-statistic:                     26.06\n",
      "Date:                Wed, 14 Sep 2022   Prob (F-statistic):               0.00\n",
      "Time:                        10:50:18   Log-Likelihood:                -44444.\n",
      "No. Observations:                5441   AIC:                         8.909e+04\n",
      "Df Residuals:                    5338   BIC:                         8.977e+04\n",
      "Df Model:                         102                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        598.1816     13.813     43.304      0.000     571.102     625.262\n",
      "treatment     64.4077     28.691      2.245      0.025       8.161     120.654\n",
      "ahgage1     -112.9107     21.596     -5.228      0.000    -155.247     -70.575\n",
      "adocond       -4.7132     12.623     -0.373      0.709     -29.459      20.032\n",
      "adosecno     -15.8171     12.035     -1.314      0.189     -39.410       7.776\n",
      "achu_sf       -9.3632     12.053     -0.777      0.437     -32.992      14.266\n",
      "acpno         22.5944     12.643      1.787      0.074      -2.191      47.380\n",
      "acpu_me      -34.1194     12.101     -2.820      0.005     -57.842     -10.397\n",
      "ahspown       30.6233     13.343      2.295      0.022       4.465      56.782\n",
      "ahsmgowe      37.8755     13.451      2.816      0.005      11.507      64.244\n",
      "ahsmgfin       3.3441     13.010      0.257      0.797     -22.160      28.848\n",
      "axposml        3.2768     13.134      0.249      0.803     -22.471      29.025\n",
      "ahh0_4        84.5300     15.983      5.289      0.000      53.198     115.862\n",
      "ahh10_14     -44.7250     96.231     -0.465      0.642    -233.378     143.928\n",
      "ahhsos        14.8305     13.808      1.074      0.283     -12.239      41.900\n",
      "ahhec10       26.5794     14.975      1.775      0.076      -2.778      55.937\n",
      "ahiwscei     -23.8824     24.534     -0.973      0.330     -71.979      24.214\n",
      "ahiwsfei       0.9797     25.024      0.039      0.969     -48.078      50.038\n",
      "ahibifip       1.5125     17.724      0.085      0.932     -33.234      36.259\n",
      "ahifapti     -67.4864     21.390     -3.155      0.002    -109.420     -25.553\n",
      "ahgsex       -92.7676     15.954     -5.815      0.000    -124.044     -61.491\n",
      "ahgeab        -7.6765     12.075     -0.636      0.525     -31.349      15.996\n",
      "ahgms          0.5816     14.641      0.040      0.968     -28.120      29.283\n",
      "abncapuf      35.9068     21.445      1.674      0.094      -6.134      77.948\n",
      "abifip       -79.2486     22.153     -3.577      0.000    -122.677     -35.820\n",
      "aoidvryf     -21.0623     21.646     -0.973      0.331     -63.497      21.372\n",
      "aoirntf      -31.3133     18.004     -1.739      0.082     -66.609       3.982\n",
      "awscef        -8.0216     19.578     -0.410      0.682     -46.402      30.359\n",
      "awscoef       19.5257     25.509      0.765      0.444     -30.482      69.533\n",
      "awsfef        12.4797     16.922      0.737      0.461     -20.695      45.655\n",
      "abiff        -35.1235     17.100     -2.054      0.040     -68.646      -1.601\n",
      "aoifinf       20.5737     21.267      0.967      0.333     -21.118      62.265\n",
      "atifditp     120.7419     41.795      2.889      0.004      38.807     202.677\n",
      "atxtottp      36.5125     39.741      0.919      0.358     -41.397     114.422\n",
      "ahhd5_9       96.0583     14.660      6.552      0.000      67.319     124.798\n",
      "ahhd1014     107.4886     96.325      1.116      0.265     -81.348     296.325\n",
      "ahhura       -14.7716     13.131     -1.125      0.261     -40.514      10.971\n",
      "afmagelh      21.4295     13.493      1.588      0.112      -5.022      47.881\n",
      "aedhists      -9.9739     14.411     -0.692      0.489     -38.226      18.278\n",
      "aedqobd        4.5214     12.927      0.350      0.727     -20.821      29.864\n",
      "aedqoms        5.8829     12.621      0.466      0.641     -18.858      30.624\n",
      "aedqodc       82.8375     12.466      6.645      0.000      58.400     107.275\n",
      "aehtjbyr    -127.6212     18.096     -7.052      0.000    -163.097     -92.145\n",
      "aehtujyr     -51.1468     12.911     -3.961      0.000     -76.458     -25.835\n",
      "aujljhru       2.9247     11.951      0.245      0.807     -20.505      26.354\n",
      "ajbprhr       23.2441     12.390      1.876      0.061      -1.045      47.533\n",
      "ajbmday      -10.2490     12.999     -0.788      0.430     -35.731      15.233\n",
      "ajbmsch       -9.3210     12.504     -0.745      0.456     -33.835      15.193\n",
      "ajbmhrh      -18.3772     12.448     -1.476      0.140     -42.781       6.027\n",
      "ajbmploj     -17.7912     11.849     -1.501      0.133     -41.021       5.438\n",
      "ajbmpgj       39.5954     12.282      3.224      0.001      15.518      63.673\n",
      "ajbmwpsz      28.6579     13.291      2.156      0.031       2.602      54.714\n",
      "artiage1      25.1636     13.756      1.829      0.067      -1.803      52.131\n",
      "ajsl4wk       -3.9712     12.887     -0.308      0.758     -29.235      21.293\n",
      "awslya        30.1178     11.975      2.515      0.012       6.641      53.594\n",
      "abncyth        4.8425     11.791      0.411      0.681     -18.272      27.957\n",
      "abifinc       47.9334     34.898      1.374      0.170     -20.481     116.348\n",
      "abifuinc      25.3946     34.141      0.744      0.457     -41.536      92.325\n",
      "abnfdsp      -36.2725     12.412     -2.922      0.003     -60.604     -11.941\n",
      "aoifsup       13.9651     16.111      0.867      0.386     -17.618      45.549\n",
      "aoifirr        3.2939     11.775      0.280      0.780     -19.790      26.378\n",
      "aoifrsv        0.9431     11.771      0.080      0.936     -22.134      24.020\n",
      "aoifpub       15.7137     11.901      1.320      0.187      -7.616      39.044\n",
      "ancsex1        8.0330     11.811      0.680      0.496     -15.121      31.187\n",
      "aicprob       50.0154     13.257      3.773      0.000      24.027      76.004\n",
      "ahelthyr      -4.7002     11.810     -0.398      0.691     -27.852      18.452\n",
      "alosateo      22.2972     13.243      1.684      0.092      -3.665      48.259\n",
      "aloimpew      10.3947     14.435      0.720      0.471     -17.904      38.694\n",
      "aloimprl     -24.7113     12.474     -1.981      0.048     -49.166      -0.257\n",
      "amhn10yr      13.6554     12.697      1.075      0.282     -11.236      38.547\n",
      "amhreawp       2.8167     11.847      0.238      0.812     -20.409      26.043\n",
      "amhrearo      10.8522     11.858      0.915      0.360     -12.393      34.098\n",
      "ajbmo61      -17.9229     17.674     -1.014      0.311     -52.572      16.726\n",
      "ajbmo6s       32.8219     19.573      1.677      0.094      -5.548      71.192\n",
      "artage         6.3630     13.971      0.455      0.649     -21.026      33.752\n",
      "aujljin1      10.0140     12.056      0.831      0.406     -13.620      33.648\n",
      "ajbempt      -62.4494     13.706     -4.556      0.000     -89.319     -35.580\n",
      "ajbcasab      26.1880     13.038      2.009      0.045       0.628      51.748\n",
      "ahsyrcad     -36.9405     15.225     -2.426      0.015     -66.788      -7.093\n",
      "atcnr        -39.3515     16.809     -2.341      0.019     -72.303      -6.400\n",
      "ahhyng       -12.2531     23.430     -0.523      0.601     -58.185      33.679\n",
      "agh3a         62.8163     14.146      4.441      0.000      35.085      90.548\n",
      "agh8           6.3458     13.771      0.461      0.645     -20.651      33.343\n",
      "alstbca      -20.0040     11.866     -1.686      0.092     -43.266       3.258\n",
      "alshrcom      -0.2661     13.757     -0.019      0.985     -27.236      26.704\n",
      "aatwkwms     -12.3584     12.778     -0.967      0.333     -37.408      12.691\n",
      "aatwkmsw     -14.2843     13.292     -1.075      0.283     -40.342      11.774\n",
      "apashare      28.8690     13.371      2.159      0.031       2.657      55.081\n",
      "apawkmfh      25.5467     12.145      2.103      0.035       1.737      49.357\n",
      "apawkbp      -14.3041     11.884     -1.204      0.229     -37.601       8.993\n",
      "aedqunk       -1.1143     11.935     -0.093      0.926     -24.512      22.283\n",
      "abnfnis     -107.4101     20.855     -5.150      0.000    -148.294     -66.526\n",
      "awscme       177.7575     25.387      7.002      0.000     127.989     227.526\n",
      "awsfe        -89.0041     39.007     -2.282      0.023    -165.475     -12.533\n",
      "abifn         25.6728     16.647      1.542      0.123      -6.962      58.308\n",
      "aoiint        -8.3112     15.325     -0.542      0.588     -38.355      21.732\n",
      "aoidvry      -10.3471     18.361     -0.564      0.573     -46.343      25.649\n",
      "aoifinvp     -70.0310     28.922     -2.421      0.015    -126.730     -13.332\n",
      "aoifpp       -32.4810     16.805     -1.933      0.053     -65.425       0.463\n",
      "atifmktp      25.8695     34.915      0.741      0.459     -42.579      94.318\n",
      "atifprin      -6.7175     16.128     -0.416      0.677     -38.336      24.901\n",
      "abnfapt       50.6752     25.050      2.023      0.043       1.566      99.784\n",
      "aoifnpt       -2.6156     11.892     -0.220      0.826     -25.928      20.697\n",
      "==============================================================================\n",
      "Omnibus:                     4145.086   Durbin-Watson:                   1.955\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           219542.436\n",
      "Skew:                           3.151   Prob(JB):                         0.00\n",
      "Kurtosis:                      33.474   Cond. No.                         32.4\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "Xt = np.hstack((t[:, np.newaxis], X))\n",
    "Xt = pd.DataFrame(data=Xt, columns=[\"treatment\"] + features)\n",
    "ols = sm.OLS(y, sm.add_constant(Xt))\n",
    "res = ols.fit()\n",
    "ate_ols = res.params.loc[\"treatment\"]\n",
    "ci_ols = res.conf_int().loc[\"treatment\"]\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4645",
   "metadata": {},
   "source": [
    "## Scikit learn Bayesian Estimators\n",
    "\n",
    "### Bayesian Ridge\n",
    "\n",
    "Coefficient statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4646",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bayesian Ridge simple model - coefficient stats:\n",
      "  R-squared = 0.3299\n",
      "  ATE: 45.2281 (22.7708)\n",
      "  t: 1.9862\n",
      "  p-value: 0.0471\n",
      "  CI (0.025, 0.975): [0.5981, 89.8580]\n"
     ]
    }
   ],
   "source": [
    "blr = BayesianRidgeStat()\n",
    "blr.fit(Xt, y)\n",
    "\n",
    "score = blr.score(Xt, y)\n",
    "\n",
    "# Coefficient statistics\n",
    "stats = blr.model_statistics()\n",
    "ate_blr, se_blr = stats.beta[0], stats.std_err[0]\n",
    "ci_blr = norm.interval(loc=ate_blr, scale=se_blr, alpha=0.95)\n",
    "\n",
    "print(\"Bayesian Ridge simple model - coefficient stats:\")\n",
    "print(f\"  R-squared = {score:.4f}\")\n",
    "print(f\"  ATE: {ate_blr:.4f} ({se_blr:.4f})\")\n",
    "print(f\"  t: {stats.t_stat[0]:.4f}\")\n",
    "print(f\"  p-value: {stats.p_value[0]:.4f}\")\n",
    "print(f\"  CI (0.025, 0.975): [{ci_blr[0]:.4f}, {ci_blr[1]:.4f}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4647",
   "metadata": {},
   "source": [
    "ATE sampling with counterfactual models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4648",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bayesian Ridge simple model - counterfactual sampling:\n",
      "  R-squared = 0.3299\n",
      "  ATE: 44.6436 (21.6335)\n",
      "  CI (0.025, 0.975): [2.2428, 87.0444]\n"
     ]
    }
   ],
   "source": [
    "# ATE sampling\n",
    "samples = 100\n",
    "w_samples = np.random.multivariate_normal(mean=blr.coef_, cov=blr.sigma_, size=samples).T\n",
    "\n",
    "n = len(X)\n",
    "Xt0 = pd.DataFrame(data=np.hstack((np.zeros((n, 1)), X)), columns=[\"treatment\"] + features)\n",
    "Xt1 = pd.DataFrame(data=np.hstack((np.ones((n, 1)), X)), columns=[\"treatment\"] + features)\n",
    "\n",
    "ate_blr_samples = np.mean(Xt1 @ w_samples, axis=0) - np.mean(Xt0 @ w_samples, axis=0)\n",
    "ate_blr = ate_blr_samples.mean()\n",
    "se_blr = np.std(ate_blr_samples, ddof=1)\n",
    "ci_blr = norm.interval(loc=ate_blr, scale=se_blr, alpha=0.95)\n",
    "\n",
    "print(\"Bayesian Ridge simple model - counterfactual sampling:\")\n",
    "print(f\"  R-squared = {score:.4f}\")\n",
    "print(f\"  ATE: {ate_blr:.4f} ({se_blr:.4f})\")\n",
    "print(f\"  CI (0.025, 0.975): [{ci_blr[0]:.4f}, {ci_blr[1]:.4f}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4649",
   "metadata": {},
   "source": [
    "### Gaussian Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4650",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "614.7303804447712"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4651",
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = WhiteKernel() + Matern(nu=1.5)\n",
    "gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True)\n",
    "\n",
    "# This takes a while for 5000 samples... (5 mins or so)\n",
    "gpr.fit(Xt, y)\n",
    "score = gpr.score(Xt, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4652",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian Process WhiteKernel(noise_level=0.364) + Matern(length_scale=12.2, nu=1.5):\n",
      "  R-squared = 0.7620\n",
      "  ATE: 53.9606 (23.2643)\n",
      "  CI (0.025, 0.975): [8.3634, 99.5578]\n"
     ]
    }
   ],
   "source": [
    "# ATE sampling   \n",
    "f0, K0 = gpr.predict(Xt0, return_cov=True)\n",
    "f1, K1 = gpr.predict(Xt1, return_cov=True)\n",
    "\n",
    "y_0_samples = np.random.multivariate_normal(mean=f0, cov=K0, size=samples)\n",
    "y_1_samples = np.random.multivariate_normal(mean=f1, cov=K1, size=samples)\n",
    "ate_gp_samples = (y_1_samples - y_0_samples).mean(axis=1)\n",
    "\n",
    "ate_gp = ate_gp_samples.mean()\n",
    "se_gp = np.std(ate_gp_samples, ddof=1)\n",
    "ci_gp = norm.interval(loc=ate_gp, scale=se_gp, alpha=0.95)\n",
    "\n",
    "print(f\"Gaussian Process {gpr.kernel_}:\")\n",
    "print(f\"  R-squared = {score:.4f}\")\n",
    "print(f\"  ATE: {ate_gp:.4f} ({se_gp:.4f})\")\n",
    "print(f\"  CI (0.025, 0.975): [{ci_gp[0]:.4f}, {ci_gp[1]:.4f}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4653",
   "metadata": {},
   "source": [
    "Check if GP is overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4654",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "if True: #xval_gp:\n",
    "    cv_scores = cross_validate(gpr, Xt, y,\n",
    "                               cv=KFold(n_splits=5, shuffle=True),\n",
    "                               return_train_score=True)\n",
    "    pd.DataFrame(cv_scores).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4655",
   "metadata": {},
   "source": [
    "## Hierarchical Bayesian Linear Model\n",
    "\n",
    "This model takes the following form and prior settings,\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "    \\{\\lambda_0, \\lambda_t, \\lambda_x, \\lambda_{tx}\\} &\\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\sigma^2 &\\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    w_0 &\\sim \\mathcal{N}(0, \\lambda_0) \\\\\n",
    "    w_t &\\sim \\mathcal{N}(0, \\lambda_t) \\\\\n",
    "    \\mathbf{w}_x &\\sim \\mathcal{N}(0, \\lambda_x \\mathbf{I}_d) \\\\\n",
    "    \\mathbf{w}_{tx} &\\sim \\mathcal{N}(0, \\lambda_{tx} \\mathbf{I}_d) \\\\\n",
    "    y_i &\\sim \\mathcal{N}(\\mu(\\mathbf{x}_i, t_i), \\sigma^2) \\\\\n",
    "    \\mu(\\mathbf{x}_i, t_i) &= w_0 + w_t t_i + \\mathbf{w}_x^\\top\\mathbf{x}_i + t_i\\mathbf{w}_{tx}^\\top\\mathbf{x}_i\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4656",
   "metadata": {},
   "source": [
    "### Set up the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4657",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(w_0, w_t, w_x, w_tx, x, t):\n",
    "    f = w_0 + w_t * t + x.matmul(w_x.T) + t * x.matmul(w_tx.T)\n",
    "    return f\n",
    "\n",
    "\n",
    "def model_treatment_intersection(x, t, y):\n",
    "    # Hyper-Priors\n",
    "    lambda_prior = dist.Gamma(1., 1.)\n",
    "    sigma_prior = dist.Gamma(1., 1.)\n",
    "    \n",
    "    # Priors\n",
    "    n, d = x.shape\n",
    "    weight_prior = dist.Laplace if laplace_prior else dist.Normal\n",
    "    p_w0 = weight_prior(0, pyro.sample(\"l_0\", lambda_prior))\n",
    "    p_wt = weight_prior(0, pyro.sample(\"l_t\", lambda_prior))\n",
    "    p_wx = weight_prior(torch.zeros(d), pyro.sample(\"l_x\", lambda_prior) * torch.ones(d))\n",
    "    p_twx = weight_prior(torch.zeros(d), pyro.sample(\"l_tx\", lambda_prior) * torch.ones(d))\n",
    "    \n",
    "    # Model weights\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",
    "    f = predict(w_0, w_t, w_x, w_tx, x, t)\n",
    "    sigma = pyro.sample(\"variance\", sigma_prior)\n",
    "    \n",
    "    with pyro.plate(\"data\", n):\n",
    "        likelihood = dist.Normal(f, sigma)\n",
    "        y = pyro.sample(\"likelihood\", likelihood, obs=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4658",
   "metadata": {},
   "source": [
    "### Run MCMC inference to compute the posteriors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4659",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warmup:   0%|                                                                                   | 0/7000 [00:00, ?it/s]C:\\Users\\annaz\\AppData\\Local\\Temp\\ipykernel_21360\\112910339.py:2: UserWarning: The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matricesor `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at  ..\\aten\\src\\ATen\\native\\TensorShape.cpp:2985.)\n",
      "  f = w_0 + w_t * t + x.matmul(w_x.T) + t * x.matmul(w_tx.T)\n",
      "Sample: 100%|███████████████████████████████████████| 7000/7000 [21:54,  5.32it/s, step size=1.69e-01, acc. prob=0.813]\n"
     ]
    }
   ],
   "source": [
    "samples = 2000\n",
    "warm_up = 5000\n",
    "\n",
    "y_mean = y.mean()\n",
    "y_std = y.std()\n",
    "\n",
    "def stdize(y):\n",
    "    return (y - y_mean) / y_std\n",
    "\n",
    "def istdize(ys):\n",
    "    return ys * y_std + y_mean\n",
    "\n",
    "X_torch = torch.tensor(X)\n",
    "t_torch = torch.tensor(t)\n",
    "y_torch = torch.tensor(stdize(y))\n",
    "\n",
    "\n",
    "# Initialize No U-Turn Sampler\n",
    "nuts_kernel = NUTS(model_treatment_intersection, max_tree_depth=7)\n",
    "model_mcmc = MCMC(nuts_kernel, num_samples=samples, warmup_steps=warm_up)\n",
    "\n",
    "# Run the sampler\n",
    "model_mcmc.run(X_torch, t_torch, y_torch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4660",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "\n",
    "# t1 = np.array(t, dtype=np.float64)\n",
    "# t_torch1 = torch.tensor(t1)\n",
    "# print(type(t1))\n",
    "# print(t1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4661",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.12.1+cpu\n",
      "1.23.2\n"
     ]
    }
   ],
   "source": [
    "print(torch.__version__)\n",
    "print(np.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4662",
   "metadata": {},
   "source": [
    "### Sample the ATE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4663",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hierarchical Linear Regression\n",
      "  R-squared = 0.3220 (0.0026)\n",
      "  ATE: 45.7381\n",
      "  CI (0.025, 0.975): [-9.5015, 113.5279]\n"
     ]
    }
   ],
   "source": [
    "hbr_samples = model_mcmc.get_samples()\n",
    "w_0s = hbr_samples[\"intercept\"]\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",
    "t0 = torch.zeros_like(t_torch)\n",
    "t1 = torch.ones_like(t_torch)\n",
    "\n",
    "for s in range(samples):\n",
    "    f = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], X_torch, t_torch)\n",
    "    f1 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], X_torch, t1)\n",
    "    f0 = predict(w_0s[s], w_ts[s], w_xs[s], w_txs[s], X_torch, t0)\n",
    "    ate_hlr_samples[s] = istdize(f1.mean()) - istdize(f0.mean())\n",
    "    score_samples[s] = r2_score(y, istdize(f))\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 Linear Regression\")\n",
    "print(f\"  R-squared = {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}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4664",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d73gH06ZNY6ONNuJ1r3vdWn2uEmdUJEmSpEFavnw5s2fP5p577mHXXXflySef5Oqrr+aQQw7h4osv5ve//z3HHXccO++8M/vttx9XXnklX/va11i0aBE//OEPV5/n4YcfZtasWdx+++284AUvYN999+Wpp57i2muv5ZBDDuELX/gCc+bMWavt973vffT29rLDDjvwyle+ksWLF3P99dfz6U9/mssuu4xLLrmE8ePHr9PnhQsXsvPOOzNp0iTe8IY38PDDD3Pttddy8MEHc9FFF7HffvuN+M9tMJxRkSRJkgbp2muvZaONNuLOO+/k5z//Ob/4xS/4+te/zsqVK/ngBz/IySefzIIFC7jmmms4//zzueWWW9hyyy350Y9+xB//+MfV53nve9/L7bffznHHHcef/vQnLrzwQi699FJuueUWtttuO44//nhuueWWtdr+1re+xUMPPcR1113H2WefzcUXX8y9997LAQccwIIFC9YKQvXOOuss3va2t3HPPfdw/vnnc80113DaaaexatUqTj755BH9eQ2FQUWSJEmDlwlPPDH6vjLb8vbHjx/Pd77zHabU3TzkiCOOYNq0adx999185CMfYY899li97/nPfz7vfOc7AbjiiisAuOmmm7jooovYfffdmTt3LhtssMHq47fddlu+/OUvs3LlSs4444y12j744IPp6elZq2zTTTfl1FNPBeDCCy9s2ufaOSdMWHNR1Yc//GGmTJnCddddx/Lly4fyoxgxXvolSZKkwWu8w99o0aY7Ec6YMYMXv/jFa5WNGzeOF77whTzyyCPsu+++69TZbrvtAHjwwQcBuPTSSwE46KCDiCa3cX/DG94AwA033LDOvrvuuotf/vKX3H333fT29rJq1SqyDGF33XVX0z7vvffea4UhgAkTJrDtttvyu9/9jkWLFvG85z2v5ftenwwqkiRJ0iC94AUvaFpem+lotr+2r7bgfeHChQB86lOf4lOf+lSfbT366KOrv89MPvnJT3LqqaeuDiaNlixZ0rR8q622alq+ySabrNWvqjCoSJIkSYPUbAZkMPsBVq5cCcAee+zBtttu2+dxW2yxxervf/KTn3DKKaew1VZbcdppp7Hbbrsxbdo0NthgA5YvX86GG27YZ4AZSJ+qxKAiSZKkwdtss+IyqtFms8063YPVajMchx9+OB/72McGVOf8888H4Jvf/CYHHHDAWvvqF+mPBQYVSZIkDV5EW9Z6dLN99tmHE044gQsuuGDAQeXxMhxuvfXW6+w7++yz29q/TvOuX5IkSVIH7LrrrsyePZtf//rXHHPMMSxdunSt/atWreKSSy7hqquuWl32kpe8BIBvf/vba13ideWVV/KlL31p/XR8PTGoSJIkSR3ywx/+kJ122onTTjuNF77whcyePZu3v/3t7LHHHjz3uc/lTW96E7/97W9XH/+xj32Mnp4evvGNb7DjjjtyxBFHsOeee7LXXnvxj//4jx18J+1nUJEkSZI6ZPr06Vx33XWccsopbL/99txwww1ccMEF3H///bz61a/m9NNP513vetfq41/ykpdwww03cOCBB/Loo4/ys5/9jKVLl/If//EfY25GZVSuUYmIjYH9gAOBnYEZwHjgbuBc4JTMXNpQ50TgMy1O+8XMnNNHe7sDxwO7AhOB24HTM/OsYb0RSZIkjSozZszo865aAJdffnmf+4488kiOPPLIdco32mgjjjnmGI455pgB9eHlL385P/vZz5rua9a3vtqtadXnThqVQQV4B/Cd8vvbgIuBycDuwGeBIyJir8z8a5O6V1MEmka/a9ZQRBwC/JRi9ukK4FFgNjAvImZm5rHDeSOSJEmS1jVag8py4JvAqZm5+tGbEfE8YD7wauA0ikDT6IzMnDeQRiJiCnAmxWzNYZl5Xlk+HbgKOCYifp6Zvx76W5EkSZLUaFSuUcnM72fmh+pDSln+IPDh8uWhETFxmE39A7AZcGEtpJTtPAwcV750RkWSJElqs1EZVPpxc7ndEJg6zHPVnqJzTpN984FlwD4RMWmY7UiSJEmqM1ov/Wpl23L7LPBYk/2zIuJVwCTgfuCizGy6PgXYqdze2LgjM5dHxK3A64CXsiYgSZIkSRqmsRhUji63F2fmM032/33D689FxLnAkfV3CouIycDm5cv7+2jrfoqgsg0GFUmSJKltxlRQiYi/Ad5HMZtyQsPuu4FPAhcB9wJTgD2BfwMOo1gwf0jd8ZvUff9UH032Njm2Vf9u62PXdr29vSxYsGAgp+lTb2/RneGeR2rG8TW2zJm5YsTOPbF37XN/fMcVLO9Zu6zZOHKMaaQ5xgavp6eHnp4eFi9ezLhxY3HFQPusWrUKgMWLF3e4JyNr1apVrFy5kt7e3n5va1z7f26oxkxQiYiXAz8AAvinzFxrhiMzf9BQpRf4UUT8Gvg9cHBE7J6Z19ROOZBmh9ltSZKkymv13BB1l/U5FsZEUImIrSiepTKF4mGPXxlo3cx8MCLOpJhteRNQCypL6g7bGGgWjzcut0ub7GvW1g7NyiPitp6enlfMmjVrYJ3uQ+0vRMM9j9SM42tsOWrO/BE79+RlEziq7vVpt05g8aS1f90snLvuOHKMaaQ5xgbvnnvuYfny5YwbN47Jkyd3ujuVVptJGes/pyeffJLx48ezxRZbsMsuu7Q8tqenZ1htjfqgEhFbAJdSrBOpBY7Bqt3m+Hm1gsxcHBFPUtyeeCuKp9E32qrc3jeENiVJkipt0003ZdGiRTz88MNA8cHTS8Caq136VduONatWraK3t3f1WNh0001HvM1RHVQiYlOKNScvA84D3p9Dm4+aUm4bZ0ZupljH8hoagkpEbADsCDwD3DGENiVJkipt6tSp9Pb2smzZMh544IFOd6fSVq5cCcD48eM73JORN2nSJKZOHe5TQPo3aiNxRGwIXEhx161fAUdk5sohnCdYs4i+8TbFtWsjDm9S9QCKWxxflpnLBtuuJElS1Y0fP55tttmGqVOnMnHicJ+jPbb19vYOe/F41U2cOJGpU6eyzTbbrJdANipnVCJiPPBj4I3AlcChmbm8xfFbAH8D/KT+lsURsQnw78AuwEPA+Q1VzwA+DRwUEYfWnk4fEVtS3C0M4JS2vClJkqQKGj9+PFtuuSVbbrklmenC+j7U7oC18847d7YjIyQiKP6+v/6MyqACfIQ1syCPAt/o4wf3ycx8lOL2wWcBX4uIP1CsKdmc4pKuqcATwOGZudZtiDPzsYg4CjgbOCciflO2t09Z/6uZeVlb35kkSVJFdeLD6mjjGp72Ga1BZUrd94f0eRScSBEsFgFfBHYFXgy8ClgJ/AmYB5yamX9pdoLMPDci9gSOL+tPBP4AnJ6ZZw7nTUiSJElqblQGlcw8kSKEDPT4JcCcYbR3NfCWodaXJEmSNDjOTUmSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqnAmd7oAkdaMZc+Z3uguSJFWaMyqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKmdCpzsgSeo+M+bMX6dszswVABzVZF87LZy7/4ieX5LUHs6oSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaqcCZ3ugCR1yow58zvdBUmS1AdnVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVzqgMKhGxcUQcHBHfjYhbImJxRPRGxM0R8a8RsUmLuu+OiOsjYmlEPBYRv4yI3ftpb/fyuMfKetdHxHva/84kSZIkwSgNKsA7gPOBoyjew8XAlcCLgM8CN0TElo2VIuIU4CxgR+C/gOuBfYErIuKQZg2V5VcAbwZuKdvaHphXnk+SJElSm43WoLIc+CbwkszcMTPfmplvBl4K/A/wMuC0+goRMQs4BlgEzMzMg8s6ewIrgTMjYkpDnSnAmcB44PDM3DszDy/PfzdwTES8cQTfpyRJktSVRmVQyczvZ+aHMvOuhvIHgQ+XLw+NiIl1uz9Rbk+ur5eZ1wLfAjajmKGp9w9l+YWZeV5dnYeB48qXxw73/UiSJEla26gMKv24udxuCEwFiIhJwOyy/JwmdWplBzaUH9CiznxgGbBPeX5JkiRJbTIWg8q25fZZ4LHy+5dRBJdHMvP+JnVuLLc7NZTv1LB/tcxcDtwKTKK45EySJElSm0zodAdGwNHl9uLMfKb8fpty2yykkJm9EfEEMCUiNs3MJRExGdi8Vb2y/HXl+W/u4xhJUoXMmDO/o+0vnLt/R9uXpNFiTAWViPgb4H0Usykn1O2q3a74qRbVeymCySbAkro6rer1Npy/v/7d1seu7Xp7e1mwYMFATtOn3t6iO8M9j9TMWBxfc2au6HQXxqSJvWv/XD++4wqW9/T/s96ivIh2rP93GUv/D402Y/HfMVWH42tdtZ/JUI2ZS78i4uXAD4AA/ikz62c4otxmq1P083ogdSRJkiS1wZiYUYmIrSiebzIFOCUzv9JwyJJy29PiNBuX26UNdWr7Fg+gTkuZuUOz8oi4raen5xWzZs0ayGn6VEvwwz2P1MxYHF9HdfgSoLFq8rIJa91C8bRbJ7B4Uv+/bmozKXNvHhO/mvq0cO7Y+X9otBmL/46pOhxf6+rpafXRu3+jfkYlIrYALqVYJ3Im8Mkmh91Xbrfq4xw9FJd9PZGZSwAyczHwZKt6deX39bFfkiRJ0hCM6qASEZsCF1Hc1es84P2Z2ezyrjuAZ4Bp5exLo9eU21saym9u2F/f9gYUT7h/pjy/JEmSpDYZtUElIjYELqS469avgCMyc2WzYzPzaaC2sunwJofUyn7RUD6/YX+9AyhuTXxZZi4bRNclSZIk9WNUBpWIGA/8GHgjcCVwaPlck1ZOKbfHR8T2defaDfgAxRqU7zbUOaMsPygiDq2rsyXwbw3nlSRJktQmo3XF4keAQ8rvHwW+EdH0BlyfzMxHATLzvyLiKxTPWbkpIi4FJgL7UgS2d2bmY/WVM/OxiDgKOBs4JyJ+U7a3D8Walq9m5mXtfnOSJElStxutQWVK3feH9HkUnEgRLADIzI9HxE0UQWdfiuetXAacnJlXNTtBZp4bEXsCxwO7UoSbPwCnZ+aZw3gPkiRJkvowKoNKZp5IEUKGUnceMG+Qda4G3jKU9iRJkiQN3qhcoyJJkiRpbDOoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaqcCZ3ugCRJ3WTGnPkdbX/h3P072r4kDZQzKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXK8PbHUxQZzm9Q5M1cAcFQbb63qbVIlSVJfnFGRJEmSVDkGFUmSJEmVY1CRJEmSVDkGFUmSJEmVs94W00fEy4Adgfsy8/r11a4kSZKk0aetMyoR8baIWBARuzSUzwVuA34CXBsRP40IZ3MkSZIkNdXusPAu4NXATbWCMrQcBywB/h+wEDgUOKLNbUuSJEkaI9odVHYEbsnMZ+rK3g0k8NbMfCfwOorQ8n+H01BEvDYi5kTEeRHxl4jIiFjW4vgTy2P6+prbou7uEfHLiHgsIpZGxPUR8Z7h9F+SJElS39q9RmVL4NqGsjcCf83MSwAy8/GIuBJ47TDbOgE4aAj1rgbublL+u2YHR8QhwE8pQt0VwKPAbGBeRMzMzGOH0AdJkiRJLbQ7qDwFbFx7ERHPAV5K8UG/3hPAlGG2dS1wM3BD+fXQAOudkZnzBnJgREwBzgTGA4dl5nll+XTgKuCYiPh5Zv56kH2XJEmS1EK7g8ofgd0iYoPMfJZiLQrAJQ3HPRf463Aayswv1r+OiOGcri//AGwGXFgLKWXbD0fEccB5wLGAQUWSJElqo3avUfkeMA24IiJOAb4ELAUurB0QERMo1qnc2ea2R8IB5facJvvmA8uAfSJi0vrrkiRJkjT2tXtG5bsUa1LeCuwC9ALvz8xFdcccSDFLsaDNbQ/UrIh4FTAJuB+4KDObrk8Bdiq3NzbuyMzlEXErReh6KcVlaJIkSZLaoK1BJTNXAG+PiE9RLKz/38xc0nDYn4BDgOva2fYg/H3D689FxLnAkZm5tFYYEZOBzcuX9/dxrvspgso2GFSkQZsxZ36nuyBJkipqRJ5Mn5n3Avf2se8m6p6zsh7dDXwSuIiib1OAPYF/Aw6jWDB/SN3xm9R9/1Qf5+xtcmyfIuK2PnZt19vby4IFw5tk6u0tujPc86h7zJm5YsDHbjFp8HXUnSb2rj1GPr7jCpb39D9uHGPrRzf/jvD3pEaS42tdtZ/JULX7yfQrI+K7AzjuOxGxXn8TZeYPMvPLmXl7ZvZm5v2Z+SNgZ2ARcHBE7F7fzQGcdkRW8EuSJEndrt0zKsHAP7xX4kN+Zj4YEWdSzLa8Cbim3FV/ydrGwOIm1Wu3Yl7aZF+ztnZoVh4Rt/X09Lxi1qxZA+t0H2oJfrjnUfc4ahCXXtX+yj335hGZiNUYMnnZBI6qe33arRNYPKn/ceMYWz8Wzu3e3xH+ntRIcnytq6enZ1j1233Xr4HaDHim36PWn7vK7fNqBZm5GHiyfLlVH/Vq5feNUL8kSZKkrjTsP1tFxDYNRZs0Katv76XAfsA9w227jWoPn2ycGbmZYh3La4Db63dExAbAjhSB646R7qAkSZLUTdoxv74QyLrXh5VfrQTwnTa0PWxRPCmytoi+8TbF8ymCyuHADxr2HUBxi+NfZuayEe2kJEmS1GXaEVSuYE1Q2YviifP/28exy4EHgJ9l5vltaHtAImIL4G+An2TmM3XlmwD/TvHMl4eAxj6dAXwaOCgiDq09nT4itqS4WxjAKSPcfUmSJKnrDDuoZObete8jYhXFAxSP6rtGe0TE/sAJDcUTI6L++Syfy8z5FLcPPgv4WkT8gWJNyeYUl3RNBZ4ADs/MtW5DnJmPRcRRwNnAORHxG+BRYJ+y/lcz87I2vzVJkiSp67X71iovYoB3wGqDaRQzIfWioWxauV0EfBHYFXgx8CpgJcXDJ+cBp2bmX5o1kpnnRsSewPFl/YnAH4DTM/PMdrwRSZIkSWtr95Ppmz7kcSRk5jyKkDGQY5cAc4bR1tXAW4ZaX5IkSdLgjMjN6iNib4pF6M8DNuzjsMzM941E+5IkSZJGt7YGlYjYDLgQ2IP+H+iYgEFFkiRJ0jraPaPyRYqZlLuBbwJ3sv7WrEiSJEkaI9odVA4CHgZ2zczH2nxuSZIkSV1iXJvPtxlwjSFFkiRJ0nC0O6jcxZpbAkuSJEnSkLQ7qHwNeH1EvLLN55UkSZLURdoaVDLzDOArwEURcWREvKCd55ckSZLUHdp9e+KVtW+B75ZlfR2emTkiz3GRJEmSNLq1Oyj8meL5KJIkSZI0ZG0NKpk5o53nkyRJktSd2r2YXpIkSZKGzaAiSZIkqXLavZj+3YM5PjO/3872JUmSJI0N7V5MP4+BLaaP8jiDiiRJkqR1tDuonETzoDIO2BrYC3gRRaC5t81tS5IkSRoj2n3XrxNb7Y+IDYDTgMOBndvZtiRJkqSxY70ups/MZ4GjgaeBueuzbUmSJEmjx3q/61dmrgB+B+y7vtuWJEmSNDp06vbEzwV6OtS2JEmSpIpbr0ElIsZFxEeB3YBb1mfbkiRJkkaPdj9HZUGL3ZtQ3PHrOcAq4LPtbFuSJEnS2NHu2xPv3c/+Z4GrgJMy87I2ty1JkiRpjGh3UHlRi33LgUfLO39JkiRJUp/a/RwVH+IoSZIkadg6ddcvSZIkSerTiASViNgxIr4REb+PiEUR8Wj5/ekRseNItClJkiRp7Gj3GhUi4mjgS8B4IOp2PQfYAXh/RPxTZn6l3W1LkiRJGhvaOqMSEfsCp1IsnD8VeDUwBdgceBXwZeAZ4JSImN3OtiVJkiSNHe2eUTkWWAHsl5nXNOy7BfiniDgPuAL4BOAtiiVJkiSto91rVF4P/KZJSFktM68FLgd2aXPbkiRJksaIdgeVjYFHBnDcI+WxkiRJkrSOdgeVPwO7RcT4vg6IiAnAbuWxkiRJkrSOdgeVC4EXAmdExOTGnWXZd4BtgAva3LYkSZKkMaLdi+m/ABwKvBs4OCJ+CSwEEngRsD8wGfhjeawkSZIkraOtQSUzH4uIPYD/oAglRzQ5bD7wgcx8vJ1tS5IkSRo72v7Ax8x8ADgwIl4EvAF4frnrAeCqzPxTu9uUJEmSNLa0NahExIbAdODxMpCsE0oiYlOKh0A+lJnL29m+JEmSpLGh3Yvpj6UIJzNbHDOzPOboNrctSZIkaYxod1A5GPhTZl7V1wHlvoXAIW1uW5IkSdIY0e6gsh1w+wCOu608VpIkSZLW0e6g0gP0DuC4pyhuUyxJkiRJ6xiJJ9O/bgDHvRZ4sM1tS5IkSRoj2h1ULgG2jYiP9nVARHyY4rKvX7W5bUmSJEljRLufo/JF4F3AaRExG/g2cA/Fk+lfDPxf4EBgcXmsJElaj2bMmd/R9hfO3b+j7UsaPdr9ZPo/R8TfAucAf0sRSuoF8Cjw1sxc2M62JUmSJI0dI/Fk+isi4iUUsyezga3LXX8G/gs4IzMfb3e7kiRJksaOtgcVgMx8Avi38kuSJEmSBqXdi+klSZIkadgMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXIMKpIkSZIqx6AiSZIkqXJGbVCJiNdGxJyIOC8i/hIRGRHLBlDv3RFxfUQsjYjHIuKXEbF7P3V2L497rKx3fUS8p33vRpIkSVK9CZ3uwDCcABw0mAoRcQpwDPA0cAkwCdgX2C8i/i4zz29S5xDgpxSh7grgUWA2MC8iZmbmscN6F5IkSZLWMZqDyrXAzcAN5ddDrQ6OiFkUIWURsFtm3lWW7wZcDpwZEZdn5uN1daYAZwLjgcMy87yyfDpwFXBMRPw8M3/d5vcmSZIkdbVRe+lXZn4xMz+Tmb/IzIcHUOUT5fbkWkgpz3Mt8C1gM+Cohjr/UJZfWAspZZ2HgePKl86oSJIkSW02aoPKYETEJIrLtQDOaXJIrezAhvIDWtSZDywD9inPL0mSJKlNuiKoAC8DNgQeycz7m+y/sdzu1FC+U8P+1TJzOXArxTqXl7apn5IkSZLonqCyTbltFlLIzF7gCWBKRGwKEBGTgc1b1asr36aP/ZIkSZKGYDQvph+MTcrtUy2O6aUIJpsAS+rqtKrX23D+liLitj52bdfb28uCBQsGcpo+9fYW3RnuedQ95sxcMeBjt5g0+DrqThN71x4jH99xBct7+h83jrHu0MnfUf6e1EhyfK2r9jMZqm6ZUYlymwM4pq/XA6kjSZIkqQ26ZUZlSbntaXHMxuV2aUOd2r7FA6jTUmbu0Kw8Im7r6el5xaxZswZymj7VEvxwz6PucdSc+QM+tvZX7rk3d8s/GxqqycsmrHULxdNuncDiSf2PG8dYd1g4t3O/o/w9qZHk+FpXT0+rj97965YZlfvK7VbNdkZED8VlX09k5hKAzFwMPNmqXl35fX3slyRJkjQE3RJU7gCeAaZFRLPQ8Zpye0tD+c0N+1eLiA2AHcvz3tGmfkqSJEmiS4JKZj4N1FY2Hd7kkFrZLxrK5zfsr3cAxa2JL8vMZcPupCRJkqTVuiKolE4pt8dHxPa1wojYDfgAxRqU7zbUOaMsPygiDq2rsyXwbw3nlSRJktQmo3bFYkTsD5zQUDwxIq6re/25zJwPkJn/FRFfAY4GboqIS4GJwL4Uge2dmflY/cky87GIOAo4GzgnIn4DPArsQ7Gm5auZeVn7350kSZLU3UZtUAGmAbs0lEVD2bT6nZn58Yi4CfgIRUB5FrgMODkzr2rWSGaeGxF7AscDu1KEmz8Ap2fmmW14H5IkSZIajNqgkpnzgHnro15mXg28ZbBtSZIkSRqablqjIkmSJGmUMKhIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqhyDiiRJkqTKMahIkiRJqpwJne6AJEnqHjPmzO9Y29/bb6OOtS1p8JxRkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlWNQkSRJklQ5BhVJkiRJlTOh0x1YnyLicmCvFoe8JTMvblLv3cBHgFcAy4HrgJMz85qR6KckSWq/Ox9eAsBRc+Z3pP2Fc/fvSLvSaNVVQaXOucDSJuV/aSyIiFOAY4CngUuAScC+wH4R8XeZef5IdlSSJEnqRt0aVD6ZmQv7OygiZlGElEXAbpl5V1m+G3A5cGZEXJ6Zj49gXyVJkqSu4xqV1j5Rbk+uhRSAzLwW+BawGXBUJzomSZIkjWUGlT5ExCRgdvnynCaH1MoOXD89kiRJkrpHt1769b6ImAqsAu4ELsjM+xqOeRmwIfBIZt7f5Bw3ltudRq6bkiRJUnfq1qByfMPrf4+Iz2Xm5+rKtim3zUIKmdkbEU8AUyJi08xcMgL91Bg3o0N3npEkSaq6bgsqVwBnANcADwJbA4dTBJeTImJxZn6lPHaTcvtUi/P1ApuXx/YbVCLitj52bdfb28uCBQv6fQOt9Pb2Agz7PFp/5sxc0ekuDNgWk4rtaOqzOmNi79pj5OM7rmB5T//jxjGmkdbpMebv57HNz2Hrqv1Mhqqr1qhk5r9m5g8y84+Z+XRm3pmZnwcOLg/5bERsVH4ftWotThkt9kmSJEkaom6bUWkqMy+JiN8CrwN2BX7NmhmSnhZVNy63zZ7J0qydHZqVR8RtPT09r5g1a9YAe9xcLcEP9zxafzr10LGhqP0Fcu7N/rOh1iYvm7DW7RBPu3UCiyf1P24cYxppnR5jC+f6+3ks83PYunp6Wn2M7l9Xzaj0o3b74eeV29ri+q2aHRwRPRSXfT3h+hRJkiSpvQwqa0wpt7XZkTuAZ4BpEdEsrLym3N4y0h2TJEmSuo1BBYiIacAe5csbATLzaaC2GurwJtVqZb8Y2d5JkiRJ3adrgkpE7BoRb4yIaCifAZxPsRblZw3PTDml3B4fEdvX1dkN+ACwGPjuiHZckiRJ6kLdtGLxZcCZwIMRcSfwEMX6k9cCk4DbgPfXV8jM/4qIrwBHAzdFxKXARGBfipD3zsx8bP29BUmSJKk7dFNQ+W/gm8AuwCuA/0PxHJSbgJ8C3ywv91pLZn48Im4CPkIRUJ4FLgNOzsyr1kvPJUmSpC7TNUElM/8AfGiIdecB89rZH0mSJEl965o1KpIkSZJGD4OKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqHIOKJEmSpMoxqEiSJEmqnAmd7oAkSVI3mDFnfkfbXzh3/462Lw2WMyqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKse7fkmSJHWBTt51zDuOaSicUZEkSZJUOQYVSZIkSZVjUJEkSZJUOa5RUdfr9JOCJUmStC5nVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVjkFFkiRJUuUYVCRJkiRVzoROd0CaMWd+p7sgSZKkinFGRZIkSVLlGFQkSZIkVY5BRZIkSVLlGFQkSZIkVY5BRZIkSVLlGFQkSZIkVY5BRZIkSVLlGFQkSZIkVY5BZQAiYlJEfDYi7oyIZRHxQER8LyK26nTfJEmSpLHIJ9P3IyImAZcBuwMPAhcCM4D3AgdExG6ZeU/neihJkqRWZsyZP+JtzJm5AoCjmrS1cO7+I97+WGRQ6d+/UISUa4H9MnMpQEQcC3wZ+B6wV+e6N3zr439eSZLUvbr9s0Yn3/9oDkle+tVCRGwAfLR8+eFaSAHIzFOAW4A9I+K1neifJEmSNFYZVFp7A7A5cE9m/k+T/eeU2wPXW48kSZKkLmBQaW1mub2xj/03NhwnSZIkqQ0iMzvdh8qKiFOAY4BTM/PYJvtnAjcBN2Zmv5d/RcRtfex62QYbbDDu+c9//nC6y6pVqwAYN25w+XP5ilXDalfdYXw5rFY6XNSPWLWKzR/8y+rXTzzvBeQA/l1yjGmkOcY0kqo6viZO6Ny8xAMPPMCzzz67JDMnD6W+i+lb26TcPtXH/t6G44Zq1bPPPtt77733/nmY59mu3HoXMo0Ex5cG7IH6F3WhpR+OMY00x5hGkuNrXVvT9+fofhlUWoty29e0U/RR3lRm7jC87rRWm7EZ6XbUnRxfGmmOMY00x5hGkuOr/Vyj0tqSctvTx/6Ny+3SPvZLkiRJGgKDSmv3ldu+nkC/VcNxkiRJktrAoNLazeX2NX3sr5Xfsh76IkmSJHUNg0prVwNPAttFxKub7D+83P5i/XVJkiRJGvsMKi1k5nLg6+XLr0fE6rUqEXEssBNwVWbe0In+SZIkSWOVz1HpR0RMAi4HdgEeBK4EXli+XgTsmpl3d6yDkiRJ0hhkUBmAiNgI+GfgHRT3g34cuBg4ITOH++wTSZIkSQ0MKpIkSZIqxzUqkiRJkirHoCJJkiSpcgwqkiRJkirHoCJJkiSpcgwqkiRJkirHoDLKRcTeEZEtvq5rUXeriPheRDwQEcsi4s6IOKl8dowEFM8SiojPluNjWTlevhcRW3W6bxodIuLyfv6denMf9d4dEddHxNKIeCwifhkRu6/v/qsaIuK1ETEnIs6LiL+UY2fZAOoNehxFxO7lcY+V9a6PiPe0792oigY7xiLixH7+bZvboq5jbAAmdLoDapt7gKv6KF9HRGwHXAtMA26leJDl64ATgH0i4o2Z+cwI9VWjRBlaLwN2p3jg6YXADOC9wAERsVtmNh1jUhPnAkublP+lsSAiTgGOAZ4GLgEmAfsC+0XE32Xm+SPZUVXSCcBBg6kwlHEUEYcAP6X4Y+4VwKPAbGBeRMzMzGOH9S5UZYMeY6WrgWYP//5ds4MdYwPnc1RGuYjYG/g1cFZmHjmIer8B9gS+mplHl2UTgLOBQ4CTMvMz7e6vRpeIOIniH+5rgf0yc2lZfizwZeCKzNyrg13UKBARlwN7AS/KzIUDOH4WRUBeBOyWmXeV5bsBl1N86HxRZj4+Ql1WBUXEp4CNgRvKr4eAZzKz6VUAQxlHETEF+BOwGXBYZp5Xlk+n+GPgi4FZmfnrkXiP6qwhjLETgc8A783MeQNswzE2CF761YUiYmeKkPJX4LhaeWauAD4IPAt8NCI26EwPVQXlf/+Pli8/XAspAJl5CnALsGdEvLYT/dOY9olye3LtwyVAZl4LfIviF/xRneiYOiczv5iZn8nMX2TmwwOoMpRx9A9l+YW1D5BlnYdZ8/vSv3aPUUMYY0PhGBsEg0p3OqDc/rzx8q7yf5QrgSnA/1nfHVOlvAHYHLgnM/+nyf5zyu2B661HGvPKyw1nly/PaXKI4079GsY4OqBhf735wDKKy6Ndy6mhcowNgmtUxo7tI+ILwFSKax2vAi7OzFVNjp1Zbm/s41w3ArPK4y5vcz81egxknNQfJ/XnfRExFVgF3AlckJn3NRzzMmBD4JHMvL/JOWrjbqeR66bGgKGOo50a9q+Wmcsj4laK9ZwvBW5uU181+s2KiFdRrIG6H7goM5uuT8ExNigGlbFj9/Kr3u8j4rD6Ke/SNuW22T/e9eXb9LFf3cFxonY7vuH1v0fE5zLzc3VlLcddZvZGxBPAlIjYNDOXjEA/NfoNehxFxGSKWeQ+65XlryvP3/UfIrXa3ze8/lxEnAscWX/ZtGNs8Lz0a/R7EvgSsCvFbMpUiunu64BXApdGxGYNdTYpt0/1cc7ehuPUnRwnapcrKH6Rb0exUPWlwKeBFcBJEXF03bH9jTtw7Kl/QxlH9ePJf/c0EHcDnwR2oBgTWwPvpLiT4WHAfzYc7xgbJGdUOiwizgF2HGS1d2fm9QDl2oHG9QMLIuINFHcD2wP4MPD5+mbLbV+3fIs+ytVdHCdqi8z814aiO4HPR8RvgV8Bn42Ib2fm0/Q/7sCxp/4NZRwNZFw59rRaZv6goagX+FFE/Br4PXBwROyemdeU+x1jg+SMSufNoPjr4mC+Nu7vpJm5Evhi+fJNDbtrl0r09FG9dv5mzztQ93CcaERl5iXAbynugLNrWdzfuAPHnvo3lHG0pMm+/upI68jMB4Ezy5f1n8EcY4NkUOmwzHxdZsYgvy4f4Olra1Oe11BeW7za15PFt2o4Tt3JcaL1ofHfqZbjLiJ6KK7xfsL1KWph0OMoMxdTXE7dZz38d08Dt85nMMfY4BlUxrYp5bYxldcWZ72mj3q18lva3iONJo4TrQ+N/07dATwDTIuIZr/IHXcaiKGOoz7/3SufLbVjed472tRPjV2D/gzmGFuXQWVsO6zcNt4ib365PTAiNqzfUT4ZdQ+KxH/VyHZPFXc1xTjYLiJe3WT/4eX2F+uvSxpLImIaxb83UN6qs1ynsqAsO7xJNced+jWMcTS/YX+9AyhuP3tZZi4bdic1ZkVEAIeUL/v6DOYYGwCDyigXER8on0tQXxYR8QHgGIqFhN+q318uxL8a2JI161iIiAnAN4ANgK9l5rMj3H1VWGYuB75evvx6eakEABFxLMW94K/KzBs60T+NDhGxa0S8sfzFXV8+AzifYg3BzxqedXFKuT0+Iravq7Mb8AFgMfDdEe24xoKhjKMzyvKDIuLQujpbAv/WcF51sYjYIiLe3eQPvpsA3wR2AR6i+HeunmNsECKz1Q0xVHURsRB4PnA7cG9Z/ErgRRQPVft4Zn6tSb3tgWspbmf8+7L+zsC2wH8De5vmVT4Z93KKf3AfBK4EXli+XgTsmpl3d6yDqryIOJJiUemDFHf7eojiGuzXUvzl8DZgVmb+taHeacDRFLfwvBSYCOxL8Qe2t2bmuevnHagqImJ/4IS6ol0o/hh3fV3Z5zJzfl2d0xjkOIqIw4CzKe6+9BuKhyjvQ7Gm5auZeXRjHY0Ngxlj5R9b/kQROv5AsaZkc4pLuqYCTwAHZObVTdpxjA2QQWWUi4iPAvtR3MN7S4rZkNoHyq+2+mt3RGwNnAS8GXgO8Gfgx8Dny2lziYjYCPhn4B0U94h/HLgYOCEz/9zJvqn6IuLlwEcpfuFvTXHddi/FL/afAt/s69+bMuR8BHg58CzF86FOzkwvS+1CdaG3lfdm5rwm9QY1jiLi/1A8oHRXinDzB+D0zOyvfY1igxljEbEpxfOgdgVeDGwBrKQILxcDp2bmX1q05RgbAIOKJEmSpMpxjYokSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJIkSaocg4okSZKkyjGoSJJGpYjYJSKy/PrnuvIj68oH+nViWffEAR4/o1PvW5K6xYROd0CSpCH6+4bvv1B+fzdwVpPj31NuzwWWNuy7qeH1zU3K6jXWlyS1WWRmp/sgSdKgRMQGwAPAVOBh4LnAazPzxhZ1ar/wXpSZC/s45kTgM8BnM/PENnZZkjRIXvolSRqN3gJsAVwBfLss+/u+D5ckjTYGFUnSaFQLJT8ovwCOiIjxHeqPJKnNDCqSpFElIjYDDgCeAc7JzLuA64HpwL6d7JskqX0MKpKk0eatwCTgF5n5RFlWm1V5V0d6JElqO4OKJGm0qb/sq+b/ASuAQyJikza08ZkWtya+qQ3nlyT1w9sTS5JGjfL5JW8AHgN+WSvPzEci4lfA/sAhwH8Os6lWtye+b5jnliQNgEFFkjSavAsI4OzMXN6w7wcUQeXvGX5QucDbE0tSZxlUJEmjSW0NyuyIuKph34Z1+56XmQ+ux35JktrMoCJJGhUi4vXAS8uX25dfzYwD3gF8eX30S5I0MlxML0kaLWqL6L+UmdHsC9ivPMa7f0nSKGdQkSRVXkRMAN5Wvvxxi0MXAH8FXhURO454xyRJI8ZLvyRJo8FbgGnAHZn5P30dlJkrI+Ic4EMUsypzhtjeweUdxvry1cy8cYjnliQNgEFFkjQa1C77+n8DOPbHFEHlnRHxL5m5agjtzSy/+nIBYFCRpBEUmdnpPkiSJEnSWlyjIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKsegIkmSJKlyDCqSJEmSKuf/A7mPiVbkwlMXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4665",
   "metadata": {},
   "source": [
    "## Plot ATE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4666",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ate_labels = [\"OLS\", \"Bayesian Linear\", \"Gaussian Process\", \"Hierarchical Linear\"]\n",
    "ate = [ate_ols, ate_blr, ate_gp, ate_hlr]\n",
    "ci = [ci_ols, ci_blr, ci_gp, ci_hlr]\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": "4667",
   "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}