Optimizing the limit setting potential of a multivariate analysis using the Bayes posterior ratio

In this work we consider the problem of optimal cut selection in a multivariate analysis. When we wish to place an upper limit on the normalisation of a theoretical flux model, we show how the best detector sensitivity is found by optimizing the ratio of the average upper limit to the expected signal. In a multidimensional observable space, we find the constant Bayes posterior surface that defines an acceptance region of events yielding the best limit setting power. The calculation of the posterior using a penalized likelihood method is described.