On the Strict Determination of Hypothesis Testing Games.

摘要

Measurably parameterized subsets of the set of all probability measures on a space are examined. The setup involves an arbitrary composite null hypothesis and the complementary alternative hypothesis. Suppose that for every probability measure on the parameter space, the averaged null hypothesis measure is orthogonal to the averaged alternative hypothesis measure. Whether, there then exists a Borel set in the range space which separates the null and alternative hypotheses is explored. It is shown that, in cases usually considered in hypothesis testing, there does exist such a Borel set. The relevance to this question to Bayesian vs. classical statistics is also discussed. (Author)