Bayesian Analysis

On some difficulties with a posterior probability approximation technique

Jean-Michel Marin and Christian P. Robert

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In 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 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) 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 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.

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Bayesian Anal., Volume 3, Number 2 (2008), 427-441.

First available in Project Euclid: 22 June 2012

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Bayesian model choice posterior approximation reversible jump Markov Chain Monte Carlo (MCMC) pseudo-priors unbiasedness improperty


Robert, Christian P.; Marin, Jean-Michel. On some difficulties with a posterior probability approximation technique. Bayesian Anal. 3 (2008), no. 2, 427--441. doi:10.1214/08-BA316.

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