%0 Journal Article %T Use in practice of importance sampling for repeated MCMC for Poisson models %T IS for repeated MCMC for Poisson models %+ Centre de recherche en épidémiologie et santé des populations (CESP) %+ Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145) %+ Université Paris Dauphine-PSL %+ CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) %+ Queensland University of Technology [Brisbane] (QUT) %+ School of Mathematical and physical Sciences %A Gajda, Dorota %A Guihenneuc-Jouyaux, Chantal %A Rousseau, Judith %A Mengersen, Kerrie, L. %A Nur, Darfiana %< avec comité de lecture %@ 1935-7524 %J Electronic Journal of Statistics %I Shaker Heights, OH : Institute of Mathematical Statistics %V 4 %P 361-383 %8 2010 %D 2010 %R 10.1214/09-EJS527 %K MCMC %K Importance Sampling %K Poisson model %Z Statistics [stat]/Computation [stat.CO] %Z Statistics [stat]/Methodology [stat.ME] %Z Life Sciences [q-bio]/Quantitative Methods [q-bio.QM] %Z Computer Science [cs]/Bioinformatics [q-bio.QM]Journal articles %X Abstract: 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 posteriodistribution, 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. %G English %2 https://inserm.hal.science/inserm-00498871/document %2 https://inserm.hal.science/inserm-00498871/file/EJS-2009-527-Sup1a.pdf %L inserm-00498871 %U https://inserm.hal.science/inserm-00498871 %~ INSERM %~ UNIV-PARIS5 %~ CNRS %~ UNIV-DAUPHINE %~ UNIV-PSUD %~ APHP %~ CEREMADE %~ MAP5 %~ UVSQ %~ PSL %~ UNIV-PARIS-SACLAY %~ UNIV-PSUD-SACLAY %~ UNIV-PARIS %~ UP-SCIENCES %~ UNIV-DAUPHINE-PSL %~ GS-SANTE-PUBLIQUE