Bayesian Analysis

Spiked Dirichlet process prior for Bayesian multiple hypothesis testing in random effects models

David B. Dahl, Sinae Kim, and Marina Vannucci

Full-text: Open access

Abstract

We propose a Bayesian method for multiple hypothesis testing in random effects models that uses Dirichlet process (DP) priors for a nonparametric treatment of the random e®ects distribution. We consider a general model formulation which accommodates a variety of multiple treatment conditions. A key feature of our method is the use of a product of spiked distributions, i.e., mixtures of a point-mass and continuous distributions, as the centering distribution for the DP prior. Adopting these spiked centering priors readily accommodates sharp null hypotheses and allows for the estimation of the posterior probabilities of such hypotheses. Dirichlet process mixture models naturally borrow information across objects through model-based clustering while inference on single hypotheses aver- ages over clustering uncertainty. We demonstrate via a simulation study that our method yields increased sensitivity in multiple hypothesis testing and produces a lower proportion of false discoveries than other competitive methods. While our modeling framework is general, here we present an application in the context of gene expression from microarray experiments. In our application, the modeling framework allows simultaneous inference on the parameters governing differential expression and inference on the clustering of genes. We use experimental data on the transcriptional response to oxidative stress in mouse heart muscle and compare the results from our procedure with existing nonparametric Bayesian methods that provide only a ranking of the genes by their evidence for differential expression.

Article information

Source
Bayesian Anal. Volume 4, Number 4 (2009), 707-732.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340369821

Digital Object Identifier
doi:10.1214/09-BA426

Mathematical Reviews number (MathSciNet)
MR2570085

Zentralblatt MATH identifier
1330.62029

Keywords
Bayesian nonparametrics differential gene expression Dirichlet process prior DNA microarray mixture priors model-based clustering multiple hypothesis testing

Citation

Kim, Sinae; Dahl, David B.; Vannucci, Marina. Spiked Dirichlet process prior for Bayesian multiple hypothesis testing in random effects models. Bayesian Anal. 4 (2009), no. 4, 707--732. doi:10.1214/09-BA426. https://projecteuclid.org/euclid.ba/1340369821


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