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Nonparametric Bayesian Estimation of Positive False Discovery Rates
Author(s) -
Tang Yongqiang,
Ghosal Subhashis,
Roy Anindya
Publication year - 2007
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00819.x
Subject(s) - false discovery rate , dirichlet process , posterior probability , markov chain monte carlo , dirichlet distribution , mathematics , estimator , statistics , bayesian probability , null hypothesis , computer science , algorithm , biology , mathematical analysis , biochemistry , gene , boundary value problem
Summary We propose a Dirichlet process mixture model (DPMM) for the P ‐value distribution in a multiple testing problem. The DPMM allows us to obtain posterior estimates of quantities such as the proportion of true null hypothesis and the probability of rejection of a single hypothesis. We describe a Markov chain Monte Carlo algorithm for computing the posterior and the posterior estimates. We propose an estimator of the positive false discovery rate based on these posterior estimates and investigate the performance of the proposed estimator via simulation. We also apply our methodology to analyze a leukemia data set.