A generalization of the Multiple-try Metropolis algorithm for Bayesian estimation and model selection

We propose a generalization of the Multiple-try Metropolis (MTM) algorithm of Liu et al. (2000), which is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights that may be arbitrary chosen. In particular, for Bayesian estimation we also introduce a method based on weights depending on a quadratic approximation of the posterior distribution. The resulting algorithm cannot be reformulated as an MTM algorithm and leads to a comparable gain of efficiency with a lower computational effort. We also outline the extension of the proposed strategy, and then of the MTM strategy, to Bayesian model selection, casting it in a Reversible Jump framework. The approach is illustrated by real examples.