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11/08/05 Colloquium
Dr. Claudia Angelini
Istituto per le Applicazioni del Calcolo
CNR-Napoli , Italy
Istituto per le Applicazioni del Calcolo
CNR-Napoli , Italy
Bayesian Maximum A Posteriori multiple testing procedures with applications to microarray data analysis*
Abstract: We consider a Bayesian approach to multiple hypothesis testing. We propose a simple hierarchical prior on hypotheses by imposing a prior distribution on the number of false null hypotheses. The maxi- mum a posteriori (MAP) rule is applied then to ¯nd the most plausible con¯guration of true and false null hypotheses with the maximal pos- terior probability. The resulting MAP testing procedure is based on comparisons of ordered individual Bayes factors with the correspond- ing sequence of critical values, similar in spirit with the frequentist procedures operating with p-values. Closely related step-up and step-down versions of the MAP procedure are also presented. We show the connections between them and several existing Bayesian and frequentist multiple testing procedures. Finally, applications to simulated and real data from microarray experiments will illustrate the proposed approach.* Joint work with Felix Abramovich, Tel Aviv University, Tel Aviv Israel.
