David B. Dunson

Biostatistics Branch

National Institute of Environmental Health Science

Nonparametric Bayes methods for flexible regression with epidemiologic applications

In many applications, there is interest in inference on changes in the conditional distribution of a response variable given one or more predictors. Motivated by data from reproductive and molecular epidemiology studies, we develop general nonparametric Bayes methods for conditional distribution estimation and inferences, allowing both the mean and residual distribution to change flexibly with predictors. We first propose a class of kernel stick-breaking processes (KSBP) for uncountable collections of dependent random probability measures. The KSBP generalizes the Dirichlet process to allow unknown distributions and partition structures to vary flexible with predictors. Some theoretical properties are considered, and methodology is developed for posterior computation and inferences. The methods are applied to premature delivery data from a large study of pregnancy outcomes. Priors for stochastically ordered collections of distributions are also described, and illustrated using DNA damage and repair studies.

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