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Sankhya : The Indian Journal of Statistics 2006, Volume 68, Part 3, pp. 436-460

Summary: Sankhy¯a : The Indian Journal of Statistics
2006, Volume 68, Part 3, pp. 436-460
c 2006, Indian Statistical Institute
Bayesian Maximum a posteriori Multiple Testing
Felix Abramovich
Tel Aviv University, Tel Aviv, Israel
Claudia Angelini
Consiglio Nazionale delle Ricerche, Napoli, Italy
We consider a Bayesian approach to multiple hypothesis testing. A hierarchi-
cal prior model is based on imposing a prior distribution (k) on the number
of hypotheses arising from alternatives (false nulls). We then apply the maxi-
mum a posteriori (MAP) rule to find the most likely configuration of null and
alternative hypotheses. The resulting MAP procedure and its closely related
step-up and step-down versions compare ordered Bayes factors of individual
hypotheses with a sequence of critical values depending on the prior. We
discuss the relations between the proposed MAP procedure and the existing
frequentist and Bayesian counterparts. A more detailed analysis is given for
the normal data, where we show, in particular, that by choosing a specific


Source: Abramovich, Felix - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics