Recentered importance sampling with applications to Bayesian model validation

McVinish, Ross, Mengersen, Kerrie, Nur, Darfiana, Rousseau, Judith and Guihenneuc-Jouyaux, Chantal (2013) Recentered importance sampling with applications to Bayesian model validation. Journal of Computational and Graphical Statistics, 22 1: 215-228. doi:10.1080/10618600.2012.681239

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Author McVinish, Ross
Mengersen, Kerrie
Nur, Darfiana
Rousseau, Judith
Guihenneuc-Jouyaux, Chantal
Title Recentered importance sampling with applications to Bayesian model validation
Journal name Journal of Computational and Graphical Statistics   Check publisher's open access policy
ISSN 1061-8600
Publication date 2013-03
Year available 2012
Sub-type Article (original research)
DOI 10.1080/10618600.2012.681239
Volume 22
Issue 1
Start page 215
End page 228
Total pages 14
Place of publication Alexandria, VA, United States
Publisher American Statistical Association
Collection year 2014
Language eng
Abstract Since its introduction in the early 1990s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This article examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behavior of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings, and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including the Appendix and the R code for Section 3.1.2 are available online.
Keyword Curse of dimensionality
Goodness of fit
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
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Created: Wed, 03 Apr 2013, 08:42:02 EST by Dr Ross Mcvinish on behalf of School of Mathematics & Physics