 
Summary: Sankhy¯a : The Indian Journal of Statistics
2006, Volume 68, Part 3, pp. 436460
c 2006, Indian Statistical Institute
Bayesian Maximum a posteriori Multiple Testing
Procedure
Felix Abramovich
Tel Aviv University, Tel Aviv, Israel
Claudia Angelini
Consiglio Nazionale delle Ricerche, Napoli, Italy
Abstract
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
stepup and stepdown 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
