This manuscript aims at expanding the armory for decision making under uncertainty with complex models, focusing on trying to expand the reach of decision theoretic, frequentist methods. In prior work an efficient integration method was re-evaluated for repeated calculation of statistical integrals for a set of of hypotheses (e.g., p-values, confidence intervals). Key to the method was the use of importance sampling. Subsequently, pointwise mutual information was proposed as an efficient test

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... atistics and shown to be optimal under certain conditions. Here, proposals are made for optimal frequentist test statistics that can take into account prior knowledge and that could deal with nuisance parameters.