Implicitly adaptive importance sampling

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In...

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Bibliographic Details
Published in:Statistics and computing 2021, Vol.31 (2), Article 16
Main Authors: Paananen, Topi, Piironen, Juho, Bürkner, Paul-Christian, Vehtari, Aki
Format: Article
Language:English
Subjects:
Adaptive sampling
Artificial Intelligence
Computer Science
Importance sampling
Probability and Statistics in Computer Science
Sampling methods
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
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Summary:Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In this work, we present an implicit adaptive importance sampling method that applies to complicated distributions which are not available in closed form. The method iteratively matches the moments of a set of Monte Carlo draws to weighted moments based on importance weights. We apply the method to Bayesian leave-one-out cross-validation and show that it performs better than many existing parametric adaptive importance sampling methods while being computationally inexpensive.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-020-09982-2