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February 2019 Generalized Multiple Importance Sampling
Víctor Elvira, Luca Martino, David Luengo, Mónica F. Bugallo
Statist. Sci. 34(1): 129-155 (February 2019). DOI: 10.1214/18-STS668


Importance sampling (IS) methods are broadly used to approximate posterior distributions or their moments. In the standard IS approach, samples are drawn from a single proposal distribution and weighted adequately. However, since the performance in IS depends on the mismatch between the targeted and the proposal distributions, several proposal densities are often employed for the generation of samples. Under this multiple importance sampling (MIS) scenario, extensive literature has addressed the selection and adaptation of the proposal distributions, interpreting the sampling and weighting steps in different ways. In this paper, we establish a novel general framework with sampling and weighting procedures when more than one proposal is available. The new framework encompasses most relevant MIS schemes in the literature, and novel valid schemes appear naturally. All the MIS schemes are compared and ranked in terms of the variance of the associated estimators. Finally, we provide illustrative examples revealing that, even with a good choice of the proposal densities, a careful interpretation of the sampling and weighting procedures can make a significant difference in the performance of the method.


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Víctor Elvira. Luca Martino. David Luengo. Mónica F. Bugallo. "Generalized Multiple Importance Sampling." Statist. Sci. 34 (1) 129 - 155, February 2019.


Published: February 2019
First available in Project Euclid: 12 April 2019

zbMATH: 07110683
MathSciNet: MR3938972
Digital Object Identifier: 10.1214/18-STS668

Keywords: Bayesian inference , Monte Carlo methods , multiple importance sampling

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2019
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