Efficient Bayes factor estimation from the reversible jump output

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. Copyright 2006, Oxford University Press.

[1]  Tony O’Hagan.  Bayes factors , 2006 .

[2]  Xiao-Li Meng,et al.  Warp Bridge Sampling , 2002 .

[3]  Petros Dellaportas,et al.  On Bayesian model and variable selection using MCMC , 2002, Stat. Comput..

[4]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo Methods for Computing Bayes Factors , 2001 .

[5]  S. Godsill.  On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty , 2001 .

[6]  G. Nicholls,et al.  Bridge estimation of the probability density at a point , 2001 .

[7]  S. Chib,et al.  Marginal Likelihood From the Metropolis–Hastings Output , 2001 .

[8]  P. Green,et al.  Trans-dimensional Markov chain Monte Carlo , 2000 .

[9]  M. Schervish,et al.  Bayes Factors: What They are and What They are Not , 1999 .

[10]  Xiao-Li Meng,et al.  Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling , 1998 .

[11]  Simon J. Godsill,et al.  On the relationship between MCMC model uncertainty methods , 1997 .

[12]  Ming-Hui Chen,et al.  On Monte Carlo methods for estimating ratios of normalizing constants , 1997 .

[13]  Ming-Hui Chen,et al.  ESTIMATING RATIOS OF NORMALIZING CONSTANTS FOR DENSITIES WITH DIFFERENT DIMENSIONS , 1997 .

[14]  G. Casella,et al.  Rao-Blackwellisation of sampling schemes , 1996 .

[15]  Xiao-Li Meng,et al.  SIMULATING RATIOS OF NORMALIZING CONSTANTS VIA A SIMPLE IDENTITY: A THEORETICAL EXPLORATION , 1996 .

[16]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[17]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[18]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[19]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[20]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[21]  H. Jeffreys.  Some Tests of Significance, Treated by the Theory of Probability , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  H. Jeffreys.  The Theory of Probability , 1896 .