Recentered importance sampling with applications to Bayesian model validation

Ross Mcvinish (1) , Kerrie Mengersen (2) , Darfiana Nur (3) , Judith Rousseau (4, 5) , Chantal Guihenneuc-Jouyaux (6)

1 school of mathematical sciences
2 QUT - Queensland University of Technology [Brisbane]
3 School of Mathematical and physical Sciences
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
5 CREST - Centre de Recherche en Économie et Statistique
6 UPD5 Pharmacie - Faculté de Pharmacie de Paris - Université Paris Descartes

Since its introduction in the early 90's, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This paper 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 modi - cation of IS. In addition to providing new theoretical insight into the behaviour 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 appendices and the R code for Section 3.1.2 are available online.

Mots clés: curse of dimensionality; goodness of fit; importance sampling; p-values

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Ross Mcvinish, Kerrie Mengersen, Darfiana Nur, Judith Rousseau, Chantal Guihenneuc-Jouyaux. Recentered importance sampling with applications to Bayesian model validation. Journal of Computational and Graphical Statistics, 2012, pp.1-20. ⟨10.1080/10618600.2012.681239⟩. ⟨hal-00641483⟩