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Pareto smoothed importance sampling

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Bumps [julia-actions/setup-julia](https://github.com/julia-actions/setup-julia) from 1 to 2. Release notes Sourced from julia-actions/setup-julia's releases. v2.0.0 - Update to Node20 What's Changed update to node20 by @​ranocha in julia-actions/setup-julia#209 Note the rationale for...

dependencies

The latest version of the [PSIS paper](https://arxiv.org/abs/1507.02646) added new diagnostics in addition to the Pareto shape diagnostic. The new diagnostics are detailed in https://github.com/stan-dev/posterior/issues/237. This PR adds these diagnostics. It...

This PR adds the API function `expectation`, which allows one to take some expectation wrt to PSIS-smoothed weights. This is the main function needed to compute expectations wrt LOO posteriors,...

Currently, if we use PSIS for a single parameter, we get the following output: ```julia PSISResult with 1 parameters, 1000 draws, and 1 chains Pareto shape (k) diagnostic values: Count...

There are a number of methods in the literature for fitting the generalized Pareto distribution. We currently implement both the methods of [Zhang & Stephens, 2009](https://doi.org/10.1198/tech.2009.08017) (used in the PSIS...

The PSIS paper notes it is sometimes useful to compute `h`-specific (function/expectation-specific) diagnostics, which more specifically diagnose the quality of importance sampling for the expectation in question. From discussions with...

This is the simplest way to achieve the decoupling of diagnostics and smoothing needed for #21. Edit: corresponding issue is #26

Sometimes a user may want to diagnose whether importance sampling will work without smoothing the weights. This is especially useful when computing expectation-specific diagnostics (see #21).

https://arxiv.org/abs/1906.08850 introduced an adaptive importance sampling method called Importance Weighted Moment Matching. Given a target distribution `p`, it takes Monte Carlo samples `θ` from a distribution `q`, the log density...