On some difficulties with a posterior probability approximation technique
In: ISSN: 1936-0975, 2008
Online
academicJournal
Zugriff:
International audience ; In Scott (2002) and Congdon (2006, 2007), a new method is advanced to compute posterior probabilities of models under consideration. It is based solely on MCMC outputs restricted to single models, i.e., it is bypassing reversible jump and other model exploration techniques. While it is indeed possible to approximate posterior probabilities based solely on MCMC outputs from single models, as demonstrated by Gelfand and Dey (1994) and Bartolucci et al. (2006), we show that the proposals of Scott (2002) and Congdon (2006, 2007) are biased and advance several arguments towards this thesis, the primary one being the confusion between model-based posteriors and joint pseudo-posteriors. From a practical point of view, the bias in Scott's (2002) approximation appears to be much more severe than the one in Congdon's (2006), the later being often of the same magnitude as the posterior probability it approximates, although we also exhibit an example where the divergence from the true posterior probability is extreme.
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On some difficulties with a posterior probability approximation technique
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Autor/in / Beteiligte Person: | Robert, Christian ; Marin, Jean-Michel ; CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) ; Université Paris Dauphine-PSL ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) ; Centre de Recherche en Économie et Statistique (CREST) ; Ecole Nationale de la Statistique et de l'Analyse de l'Information Bruz (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS) ; Model selection in statistical learning (SELECT) ; Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO) ; Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS) ; Adap'MC, ANR ; Misgepop, ANR ; ANR-05-BLAN-0299,ADAP'MC,Méthodes de Monte Carlo Adaptatives(2005) |
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Zeitschrift: | ISSN: 1936-0975, 2008 |
Veröffentlichung: | HAL CCSD ; International Society for Bayesian Analysis, 2008 |
Medientyp: | academicJournal |
DOI: | 10.1214/08-BA316 |
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