A generalized Multiple-try Metropolis version of the Reversible Jump algorithm

Details A generalized Multiple-try Metropolis version of the Reversible Jump algorithm A generalized Multiple-try Metropolis version of the Reversible Jump algorithm

2010-06-03

arxiv.org/abs/1006.0621v1

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The Reversible Jump (RJ) algorithm (Green, 1995) is one of the most used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. We propose a generalized Multiple-try version of this algorithm which is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights (selection probabilities) that may be arbitrary chosen. Along the same lines as in Pandolfi et al. (2010), we exploit among the possible choices, a method based on selection probabilities depending on a quadratic approximation of the posterior distribution. Moreover, we extend these results by showing the implementation of an efficient transdimensional algorithm for challenging model selection problems. The resulting algorithm leads to a gain of efficiency with respect to the RJ algorithm also in terms of computational effort. We illustrate the approach by real examples involving a logistic regression model and a latent class model.

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