  The problem of testing mutually exclusive hypotheses with dependent test
statistics is considered. Bayesian and frequentist approaches to multiplicity
control are studied and compared to help gain understanding as to the effect of
test statistic dependence on each approach. The Bayesian approach is shown to
have excellent frequentist properties and is argued to be the most effective
way of obtaining frequentist multiplicity control, without sacrificing power,
when there is considerable test statistic dependence.
