The frequentist test for this attempts to see what would happen with a variety of test designs using likelihood ratio and similar statistical tests. Relaxing it

The frequentist test for this attempts to see what would happen with a variety of test designs using likelihood ratio and similar statistical tests. Relaxing it you end up with Generalized Method of Moments family. A Bayesian would attempt to compute the Bayes factor using approximate Bayesian computation resulting in more or less the same thing. You end up with various information criteria. Both approaches then converge in using Monte Carlo techniques to evaluate the features of the whole experimental setup using simulated data. All of the above approaches replace the problem of choosing the test/design based on data by the researcher with one by a data driven algorithm with known properties.