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Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments

Gomez-Villegas, Miguel Angel and Ausin, A.C and Gonzalez-Perez, B. and Rodriguez-Bernal, M.T. and Salazar, I. and Sanz San Miguel, Luis (2011) Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments. Communications in statistics. Theory and methods, 40 (13). pp. 2276-2291. ISSN 0361-0926

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Abstract

Recently, the field of multiple hypothesis testing has experienced a great expansion, basically because of the new methods developed in the field of genomics.
These new methods allow scientists to simultaneously process thousands of hypothesis tests.
The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. Alternatively, in this article, a Bayesian hierarchical model based on mixture distributions and an empirical Bayes approach are proposed in order to produce a list of rejected hypotheses that will be declared significant and interesting for a more detailed posterior analysis.
In particular, we develop a straightforward implementation of a Gibbs sampling scheme where all the conditional posterior distributions are explicit.
The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show that our model improves the FDR procedure in the sense that it diminishes the percentage of false negatives keeping an acceptable percentage of false positives.


Item Type:Article
Uncontrolled Keywords:Empirical Bayes methods; False discovery rate; Gibbs sampler; Mixture models; Multiple hypothesis testing;False Discovery Rate; Gene-Expression; Empirical Bayes; Model;Statistics & Probability
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:15635
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