Ricerc@Sapienza

In Bayesian decision theory, the performance of an action is measured by its posterior expected loss. In some cases it may be convenient/necessary to use a non-optimal decision instead of the optimal one. In these cases it is important to quantify the additional loss we incur and evaluate whether to use the non-optimal decision or not. In this article we study the predictive probability distribution of a relative measure of the additional loss and its use to define sample size determination criteria in one-sided testing.

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution.

The sample size determination problem deals with the selection of the optimal number of subjects to be enrolled in a study in order to achieve a pre-specified inferential goal. While this problem can of course be approached from a frequentist viewpoint, often the Bayesian paradigm is preferred as it allows to blend and balance the strength of the observed empirical evidence with the available prior knowledge. In this work, we focus on the case of a ''community of priors'' representing, for example, different expert opinions.