A generalized multiple-try version of the Reversible Jump algorithm

• Published in: Computational statistics & data analysis Vol. 72; pp. 298 - 314
• Main Authors: Pandolfi, Silvia, Bartolucci, Francesco, Friel, Nial
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2014
• Subjects: Algorithms; Bayesian inference; Bayesian theory; Latent class model; Logistic model; Markov chain; Markov chain Monte Carlo; Metropolis–Hastings algorithm; regression analysis; Metropolis–Hastings algorithm; Logistic model; Bayesian inference; Markov chain Monte Carlo; Latent class model
• ISSN: 0167-9473; 1872-7352; 1872-7352
• DOI: 10.1016/j.csda.2013.10.007

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 arbitrarily 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.