We give an equivalent of the Bayes risk for a general class of losses in the compact and in the non-compact cases, showing the equivalence with quadratic risks. Some examples are presented.

This paper obtains asymptotic expansions of the frequentist distributions of modified likelihood ratio statistics when the observations are discrete. An upper bound of the uncertainty due to the discrete nature of the observations is obtained, which is slightly larger than Yarnold's result...

We are interested in estimating level sets using a Bayesian non-parametric approach, from an independent and identically distributed sample drawn from an unknown distribution. Under fairly general conditions on the prior, we provide an upper bound on the rate of convergence of the Bayesian level...

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...