Sufficient dimension reduction via bayesian mixture modeling.

Dimension reduction is central to an analysis of data with many predictors. Sufficient dimension reduction aims to identify the smallest possible number of linear combinations of the predictors, called the sufficient predictors, that retain all of the information in the predictors about the response distribution. In this article, we propose a Bayesian solution for sufficient dimension reduction. We directly model the response density in terms of the sufficient predictors using a finite mixture model. This approach is computationally efficient and offers a unified framework to handle categorical predictors, missing predictors, and Bayesian variable selection. We illustrate the method using both a simulation study and an analysis of an HIV data set.