Layered adaptive importance sampling

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Martino , L , Elvira , V , Luengo , D & Corander , J 2017 , ' Layered adaptive importance sampling ' , Statistics and Computing , vol. 27 , no. 3 , pp. 599-623 .

Title: Layered adaptive importance sampling
Author: Martino, L.; Elvira, V.; Luengo, D.; Corander, J.
Contributor organization: Department of Mathematics and Statistics
Date: 2017-05
Language: eng
Number of pages: 25
Belongs to series: Statistics and Computing
ISSN: 0960-3174
Abstract: Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a layered (i.e., hierarchical) procedure to generate samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. Furthermore, we provide a general unified importance sampling (IS) framework, where multiple proposal densities are employed and several IS schemes are introduced by applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov chain Monte Carlo (MCMC) chains. The resulting algorithms efficiently combine the benefits of both IS and MCMC methods.
Subject: Bayesian inference
Adaptive importance sampling
Population Monte Carlo
Parallel MCMC
Multiple importance sampling
112 Statistics and probability
113 Computer and information sciences
Peer reviewed: Yes
Rights: other
Usage restriction: openAccess
Self-archived version: acceptedVersion

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