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The Reversible Jump algorithm is one of the most widely used Markov chainMonte Carlo algorithms for Bayesian estimation and model selection. Ageneralized multiple-try version of this algorithm is proposed. The algorithmis based on drawing several proposals at each step and randomly choosing one ofthem on the basis of weights (selection probabilities) that may be arbitrarychosen. Among the possible choices, a method is employed which is based onselection probabilities depending on a quadratic approximation of the posteriordistribution. Moreover, the implementation of the proposed algorithm forchallenging model selection problems, in which the quadratic approximation isnot feasible, is considered. The resulting algorithm leads to a gain inefficiency with respect to the Reversible Jump algorithm, and also in terms ofcomputational effort. The performance of this approach is illustrated for realexamples involving a logistic regression model and a latent class model.

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