In classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of...

In this article, a simple algorithm is provided to maximize a family of optimal statistics for hypothesis testing with a nuisance parameter not defined under the null hypothesis. This arises from genetic linkage and association studies and other hypothesis testing problems. It is known that the...