  The Reversible Jump algorithm is one of the most widely used Markov chain
Monte Carlo algorithms for Bayesian estimation and model selection. A
generalized multiple-try version of this algorithm is proposed. The algorithm
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. Among the possible choices, a method is employed which is based on
selection probabilities depending on a quadratic approximation of the posterior
distribution. Moreover, the implementation of the proposed algorithm for
challenging model selection problems, in which the quadratic approximation is
not feasible, is considered. The resulting algorithm leads to a gain in
efficiency with respect to the Reversible Jump algorithm, and also in terms of
computational effort. The performance of this approach is illustrated for real
examples involving a logistic regression model and a latent class model.
