  We investigate the efficiency of a marginal likelihood estimator where the
product of the marginal posterior distributions is used as an
importance-sampling function. The approach is generally applicable to
multi-block parameter vector settings, does not require additional Markov Chain
Monte Carlo (MCMC) sampling and is not dependent on the type of MCMC scheme
used to sample from the posterior. The proposed approach is applied to normal
regression models, finite normal mixtures and longitudinal Poisson models, and
leads to accurate marginal likelihood estimates.
