Unified Bayesian and Conditional Frequentist Testing of
Composite Hypotheses
Sarat C. Dass and James O. Berger
Testing of a composite null hypothesis versus a composite alternative
is considered when both have a related invariance structure.
The goal is to develop conditional frequentist tests that
allow the reporting of data-dependent error probabilities,
error probabilities that have a strict frequentist
interpretation and that reflect the actual amount
of evidence in the data. The
resulting tests are also seen to be Bayesian tests, in the
strong sense that the reported frequentist error probabilities
are also the posterior probabilities of the hypotheses under
default choices of the prior distribution. The new procedures
are illustrated in a variety of
applications to model selection and multivariate hypothesis
testing.