PSIS.jl
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Importance weighted moment matching
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 function of q
, and a function h
whose expectation one wants to take. It then alternates between transforming the Monte Carlo samples to θ*
(effectively, modifying the proposal distribution) and computing the Pareto shape diagnostic k
until k ≤ 0.7
. The transformations used are affine and are chosen to match the first two moments of the proposal distribution to the first 2 importance-weighted moments.
The method returns either the estimated expectation 𝔼ₚ[h(θ)]
or, perhaps, h(θ*)
and w(θ*)
, as well as the shape diagnostic. It would be handy also to return the sequence of affine transformations (or their composition) used. Like #21, this motivates some rethinking of the API.