Monte Carlo Method Implementation of the Neyman-Pearson Lemma

I haven't seen this published anywhere so thought I'd share my (possible) invention. It has some pretty useful applications such as assessing claims of quantum supremacy.

When a statistical model is too complicated for analytically precise application of the Neyman‐Pearson Lemma, the Monte Carlo method can be used to approximate the optimal critical test region of one hypothesis against another.

Notation:

The Neyman‐Pearson Lemma guarantees that this maximizes the power¹ of any statistical test of θ' vs. θ for the user‐specified false rejection rate².

Algorithm:

1. Power is defined as the probability of rejecting θ' when θ is true.

2. False rejection rate – aka significance – is defined as the probability of rejecting θ when θ is true.