Pareto Smoothed Importance Sampling

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2024
Major/Subject
Mcode
Degree programme
Language
en
Pages
58
Series
Journal of Machine Learning Research, Volume 25
Abstract
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates, and convergence diagnostics. The presented Pareto ˆk finite sample convergence rate diagnostic is useful for any Monte Carlo estimator.
Description
Keywords
Bayesian computation, Monte Carlo, Diagnostics, Importance sampling
Other note
Citation
Vehtari, A, Simpson, D, Gelman, A, Yao, Y & Gabry, J 2024, ' Pareto Smoothed Importance Sampling ', Journal of Machine Learning Research, vol. 25, 72 . < https://www.jmlr.org/papers/v25/19-556.html >