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Biostatistics Advance Access published online on August 16, 2008
Biostatistics, doi:10.1093/biostatistics/kxn024
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Bayesian hierarchically weighted finite mixture models for samples of distributions

Abel Rodriguez

Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA abel{at}ams.ucsc.edu

David B. Dunson

Biostatistics Branch, National Institute of Environmental Health Sciences, US National Institutes of Health, Research Triangle Park, NC 27709, USA

Jack Taylor

Epidemiology Branch, National Institute of Environmental Health Sciences, US National Institutes of Health, Research Triangle Park, NC 27709, USA

1 To whom correspondence should be addressed.

Finite mixtures of Gaussian distributions are known to provide an accurate approximation to any unknown density. Motivated by DNA repair studies in which data are collected for samples of cells from different individuals, we propose a class of hierarchically weighted finite mixture models. The modeling framework incorporates a collection of k Gaussian basis distributions, with the individual-specific response densities expressed as mixtures of these bases. To allow heterogeneity among individuals and predictor effects, we model the mixture weights, while treating the basis distributions as unknown but common to all distributions. This results in a flexible hierarchical model for samples of distributions. We consider analysis of variance–type structures and a parsimonious latent factor representation, which leads to simplified inferences on non-Gaussian covariance structures. Methods for posterior computation are developed, and the model is used to select genetic predictors of baseline DNA damage, susceptibility to induced damage, and rate of repair.

Keywords: Comet assay; Finite mixture model; Genotoxicity; Hierarchical functional data; Latent factor; Samples of distributions; Stochastic search

Received July 3, 2007; revised March 20, 2008; revised June 4, 2008; accepted for publication July 8, 2008.


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