Some difficulties with some posterior probability approximations

Robert, Christian P.; Marin, Jean-Michel

Robert, Christian P.; Marin, Jean-Michel (2008), Some difficulties with some posterior probability approximations, Bayesian Analysis, 3, 2, p. 427-442. http://dx.doi.org/10.1214/08-BA316

Type

Article accepté pour publication ou publié

Date

2008

Nom de la revue

Bayesian Analysis

Volume

Numéro

Pages

427-442

Résumé (EN)

n Scott (2002) and Congdon (2006), 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 approxi- mate 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) are biased and advance sev- eral 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 latter 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.