  We propose a frequentist testing procedure that maintains a defined coverage
and is optimal in the sense that it gives maximal power to detect deviations
from a null hypothesis when the alternative to the null hypothesis is sampled
from a pre-specified distribution (the prior distribution). Selecting a prior
distribution allows to tune the decision rule. This leads to an increased
power, if the true data generating distribution happens to be compatible with
the prior. It comes at the cost of losing power, if the data generating
distribution or the observed data are incompatible with the prior. We
illustrate the proposed approach for a binomial experiment, which is
sufficiently simple such that the decision sets can be illustrated in figures,
which should facilitate an intuitive understanding. The potential beyond the
simple example will be discussed: the approach is generic in that the test is
defined based on the likelihood function and the prior only. It is
comparatively simple to implement and efficient to execute, since it does not
rely on Minimax optimization. Conceptually it is interesting to note that for
constructing the testing procedure the Bayesian posterior probability
distribution is used.
