Statistica Sinica

Antonietta Mira and Geoff Nicholls

Abstract:Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block Metropolis-Hastings estimators of Chib and Jeliazkov (2001) are bridge sampling estimators. This identification leads to estimators for the quantity of interest which may be substantially more efficient.

Key words and phrases:Bayes factor, marginal likelihood, Markov chain Monte Carlo, Metropolis-Hastings algorithms.