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Abstract:
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This paper produces three new local fdr based algorithms for multiple testing of hypotheses appearing in non-overlapping groups. These algorithms, developed under a simple extension of the classical two-class mixture model from single to multiple groups that brings the underlying group structure into the hidden states of the hypotheses, are designed to answer three different questions: Q1. How to effectively capture the underlying group structure, instead of simply pooling all the hypotheses into a single group, while controlling false discoveries across all individual hypotheses? Q2. When discovering significant hypotheses within each group is an important consideration, how to maintain a control over false discoveries within each group while answering Q1? Q3. When discovering significant groups is an important consideration, as seen in selective inference, how to maintain a control over falsely discovered groups while answering Q1.?
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