## Bayesian Maximum a Posteriori Multiple Testing Procedure (2006)

Venue: | Sankhya |

Citations: | 10 - 4 self |

### BibTeX

@TECHREPORT{Abramovich06bayesianmaximum,

author = {Felix Abramovich and Claudia Angelini},

title = {Bayesian Maximum a Posteriori Multiple Testing Procedure},

institution = {Sankhya},

year = {2006}

}

### OpenURL

### Abstract

We consider a Bayesian approach to multiple hypothesis testing. A hierarchical prior model is based on imposing a prior distribution π(k) on the number of hypotheses arising from alternatives (false nulls). We then apply the maximum 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 π(k), the MAP procedure can mimic several known familywise error (FWE) and false discovery rate (FDR) controlling procedures. The performance of MAP procedures is illustrated on a simulated example. AMS (2000) subject classification. Primary 62F15, 62F03.

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