Marginal Likelihood Estimation via Power Posteriors

this paper is to illustrate how this may be achieved using ideas from thermodynamic integration or path sampling. We show how the marginal likelihood can be computed via MCMC methods on modified posterior distributions for each model. This then allows Bayes factors or posterior model probabilities to be calculated. We show that this approach requires very little tuning, and is straightforward to implement. The new method is illustrated in a variety of challenging statistical setting