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Posterior consistency of Dirichlet mixtures of beta densities in estimating positive false discovery rates

Subhashis Ghosal, Anindya Roy, and Yongqiang Tang

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Abstract

In recent years, multiple hypothesis testing has come to the forefront of statistical research, ostensibly in relation to applications in genomics and some other emerging fields. The false discovery rate (FDR) and its variants provide very important notions of errors in this context comparable to the role of error probabilities in classical testing problems. Accurate estimation of positive FDR (pFDR), a variant of the FDR, is essential in assessing and controlling this measure. In a recent paper, the authors proposed a model-based nonparametric Bayesian method of estimation of the pFDR function. In particular, the density of p-values was modeled as a mixture of decreasing beta densities and an appropriate Dirichlet process was considered as a prior on the mixing measure. The resulting procedure was shown to work well in simulations. In this paper, we provide some theoretical results in support of the beta mixture model for the density of p-values, and show that, under appropriate conditions, the resulting posterior is consistent as the number of hypotheses grows to infinity.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 105-115

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058267

Digital Object Identifier
doi:10.1214/193940307000000077

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62G10: Hypothesis testing

Keywords
Dirichlet process Dirichlet mixture multiple testing positive false discovery rate posterior consistency

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Ghosal, Subhashis; Roy, Anindya; Tang, Yongqiang. Posterior consistency of Dirichlet mixtures of beta densities in estimating positive false discovery rates. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 105--115, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000077. https://projecteuclid.org/euclid.imsc/1207058267


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