Bridge estimation of the probability density at a point

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.