On the predictive performance of a non-optimal action in hypothesis testing

In Bayesian decision theory, the performance of an action is measured by its pos- terior 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 a general testing set-up.