This dissertation studies the large-scale multiple testing problem from a compound decision theoretical view, and proposes a new class of powerful data-driven procedures that substantially outperform the traditional p -value based approaches. There are several important implications from my...

In large-scale studies, the true effect sizes often range continuously from zero to small to large, and are observed with heteroscedastic errors. In practical situations where the failure to reject small deviations from the null is inconsequential, specifying an indifference region (or forming...

The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal data-driven procedures that aim to...

In single hypothesis testing, power is a nondecreasing function of Type I error rate; hence it is desirable to test at the nominal level exactly to achieve optimal power. The optimal power puzzle arises from the fact that for multiple testing under the false discovery rate paradigm, such a...

type="main" xml:id="rssb12064-abs-0001" <title type="main">Summary</title> <p>The paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both pointwise and clusterwise spatial analyses, and derive oracle procedures which optimally...</p>