MCMC-driven adaptive multiple importance sampling

Luca Martino*, Víctor Elvira, David Luengo, Jukka Corander

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Monte Carlo (MC) methods are widely used for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling (IS) and its adaptive extensions (such as adaptive multiple IS and population MC). In this work, we introduce an iterated batch importance sampler using a population of proposal densities, which are adapted according to a Markov Chain Monte Carlo (MCMC) technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the generated samples weighted according to the so-called deterministic mixture scheme. Compared with a traditional multiple IS scheme with the same number of samples, the performance is substantially improved at the expense of a slight increase in the computational cost due to the additional MCMC steps. Moreover, the dependence on the choice of the cloud of proposals is sensibly reduced, since the proposal density in the MCMC method can be adapted in order to optimize the performance. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error.

Original languageEnglish
Title of host publicationInterdisciplinary Bayesian Statistics, EBEB 2014
EditorsAdriano Polpo, Francisco Louzada, Marcelo Lauretto, Julio Michael Stern, Laura Letícia Ramos Rifo
PublisherSpringer
Pages97-109
Number of pages13
Volume118
ISBN (Electronic)9783319124537
DOIs
Publication statusPublished - 26 Feb 2015
Event12th Brazilian Meeting on Bayesian Statistics, EBEB 2014 - Atibaia, Brazil
Duration: 10 Mar 201414 Mar 2014

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume118

Conference

Conference12th Brazilian Meeting on Bayesian Statistics, EBEB 2014
Country/TerritoryBrazil
CityAtibaia
Period10/03/1414/03/14

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