Recentered Importance Sampling With Applications to Bayesian Model Validation

Ross McVinish, Kerrie Mengersen, Darfiana Nur, Judith Rousseau, Chantal Guihenneuc-Jouyaux

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)215-228
    Number of pages14
    JournalJOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
    Volume22
    Issue number1
    DOIs
    Publication statusPublished - 2013

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