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* Remove outdated docs of Distributions integration
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Copy file name to clipboardExpand all lines: docs/src/index.md
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# PSIS
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PSIS.jl implements the Pareto smoothed importance sampling (PSIS) algorithm from [^VehtariSimpson2021].
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PSIS.jl implements the Pareto smoothed importance sampling (PSIS) algorithm from [VehtariSimpson2021](@citet).
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Given a set of importance weights used in some estimator, PSIS both improves the reliability of the estimates by smoothing the importance weights and acts as a diagnostic of the reliability of the estimates.
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When running PSIS with many parameters, it is useful to plot the Pareto shape values to diagnose convergence.
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See [Plotting PSIS results](@ref) for examples.
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[^VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021).
┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.
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└ @ PSIS ~/.julia/packages/PSIS/...
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┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples.
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└ @ PSIS ~/.julia/packages/PSIS/...
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PSISResult with 1000 draws, 1 chains, and 30 parameters
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Pareto shape (k) diagnostic values:
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Count Min. ESS
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(-Inf, 0.5] good 7 (23.3%) 959
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(0.5, 0.7] okay 13 (43.3%) 938
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(0.7, 1] bad 9 (30.0%) ——
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(1, Inf) very bad 1 (3.3%) ——
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```
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If the draws were generated using MCMC, we can compute the relative efficiency using
┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.
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└ @ PSIS ~/.julia/packages/PSIS/...
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┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples.
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└ @ PSIS ~/.julia/packages/PSIS/...
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PSISResult with 1000 draws, 1 chains, and 30 parameters
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Pareto shape (k) diagnostic values:
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Count Min. ESS
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(-Inf, 0.5] good 9 (30.0%) 806
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(0.5, 0.7] okay 11 (36.7%) 842
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(0.7, 1] bad 9 (30.0%) ——
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(1, Inf) very bad 1 (3.3%) ——
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```
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# References
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- [VehtariSimpson2021](@cite) Vehtari et al. JMLR 25:72 (2021).
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