Efficient Bayes factor estimation from the reversible jump output
1 Department of Economics, Finance and Statistics, University of Perugia, 06123 Perugia, Italy bart{at}stat.unipg.it, 2 Department of Economic and Financial Institutions, University of Macerata, 62100 Macerata, Italy scaccia{at}unimc.it, 3 Department of Economics, University of Insubria, 21100 Varese, Italy antonietta.mira{at}uninsubria.it
We propose a class of estimators of the Bayes factor which is based on an extension of the bridge sampling identity of Meng & Wong (1996) and makes use of the output of the reversible jump algorithm of Green (1995). Within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models. The proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the Bayes factor over the standard estimator based on the reversible jump output. This is illustrated through a series of Monte Carlo simulations involving a linear and a logistic regression model.
Key Words: Bayesian model choice; Bridge sampling; Marginal likelihood; Markov chain Monte Carlo; Reversible jump
Received September 2004. Revised September 2005.