
Use in practice of importance sampling for repeated MCMC for Poisson models
Gajda, Dorota; Guihenneuc-Jouyaux, Chantal; Rousseau, Judith; Mengersen, Kerrie; Nur, Darfiana (2010), Use in practice of importance sampling for repeated MCMC for Poisson models, Electronic Journal of Statistics, 4, p. 361-383. 10.1214/09-EJS527
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Article accepté pour publication ou publiéDate
2010Journal name
Electronic Journal of StatisticsVolume
4Publisher
Institute of Mathematical Statistics
Pages
361-383
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Gajda, DorotaCentre de recherche en épidémiologie et santé des populations [CESP]
Guihenneuc-Jouyaux, Chantal
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Centre de recherche en épidémiologie et santé des populations [CESP]
Rousseau, Judith
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mengersen, Kerrie
Nur, Darfiana
School of Mathematical and physical Sciences
Abstract (EN)
The Importance Sampling method is used as an alternative approach to MCMC in repeated Bayesian estimations. In the particular context of numerous data sets, MCMC algorithms have to be called on several times which may become computationally expensive. Since Importance Sampling requires a sample from a posterior distribution, our idea is to use MCMC to generate only a certain number of Markov chains and use them later in the subsequent IS estimations. For each Importance Sampling procedure, the suitable chain is selected by one of three criteria we present here. The first and second criteria are based on the L1 norm of the difference between two posterior distributions and their Kullback-Leibler divergence respectively. The third criterion results from minimizing the variance of IS estimate. A supplementary automatic selection procedure is also proposed to choose those posterior for which Markov chains will be generated and to avoid arbitrary choice of importance functions. The featured methods are illustrated in simulation studies on three types of Poisson model: simple Poisson model, Poisson regression model and Poisson regression model with extra Poisson variability. Different parameter settings are considered.Subjects / Keywords
Poisson model; Importance Sampling; MCMCRelated items
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