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<p>This thesis investigates frequentist properties of Bayesian multiple testing procedures
in a variety of scenarios and depicts the asymptotic behaviors of Bayesian methods.
Both Bayesian and frequentist approaches to multiplicity control are studied and compared,
with special focus on understanding the multiplicity control behavior in situations
of dependence between test statistics.</p><p>Chapter 2 examines a problem of testing
mutually exclusive hypotheses with dependent data. 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. Chapter 3
further generalizes the model such that multiple signals are acceptable, and depicts
the asymptotic behavior of false positives rates and the expected number of false
positives. Chapter 4 considers the problem of dealing with a sequence of different
trials concerning some medical or scientific issue, and discusses the possibilities
for multiplicity control of the sequence. Chapter 5 addresses issues and efforts in
reconciling frequentist and Bayesian approaches in sequential endpoint testing. We
consider the conditional frequentist approach in sequential endpoint testing and show
several examples in which Bayesian and frequentist methodologies cannot be made to
match.</p>
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