Bayesian hierarchically weighted finite mixture models for samples of distributions.
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.
Rodriguez
Abel
A
Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA. abel@ams.ucsc.edu
Dunson
David B
DB
Taylor
Jack
J
D000704:Analysis of Variance; D001499:Bayes Theorem; D001699:Biometry / Q000379:methods; D020552:Comet Assay; D004247:DNA / Q000032:analysis / Q000187:drug effects / Q000235:genetics; D004249:DNA Damage; D004260:DNA Repair; D005260:Female; D006801:Humans; D006861:Hydrogen Peroxide / Q000494:pharmacology; D008297:Male; D015233:Models, Statistical; D016011:Normal Distribution; D012044:Regression Analysis; D018401:Sample Size; D013269:Stochastic Processes
D004247:DNA; D006861:Hydrogen Peroxide