Bayesian Density Regression with Applications
David Dunson, Ph.D.
Institute of Statistics and Decision Sciences
National Institute of Environmental Health Sciences
Wednesday, April 11
In many applications, interest focuses on relating one or more predictors to the distribution of an outcome variable. Typically, the conditional response distribution given the predictors is unknown, but simplifying parametric assumptions are made, such as normality, linearity or a constant residual distribution. Hierarchical mixtures of experts models have been proposed, which avoid such assumptions through the use of locally-weighted mixtures of parametric models. For example, for a continuous response, a mixture of normal linear regressions could be used, with the mixture weights varying with predictor values. To avoid restrictive assumptions, such as a
known number of mixture components or a known structure for the mixture weights, we propose a general nonparametric Bayes method for uncountable collections of random probability measures indexed by predictors. Our proposed approach expresses the unknown mixture distribution as a kernel convolution of Dirichlet process basis distributions, with a random stick-breaking measure placed on the
basis locations. A key property of the proposed structure is sparceness, with the method automatically tending to favor few components. Additional properties are discussed, an efficient retrospective MCMC algorithm is developed for posterior computation, and the methods are illustrated through a reproductive epidemiology application.
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