We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.

Since its introduction in the early 90's, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This paper examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on...