Modeling Regression Error With a Mixture of Polya Trees

Abstract

We model the error distribution in the standard linear model as a mixture of absolutely continuous Polya trees constrained to have median 0. By considering a mixture, we smooth out the partitioning effects of a simple Polya tree and the predictive error density has a derivative everywhere except 0. The error distribution is centered around a standard parametric family of distributions and thus may be viewed as a generalization of standard models in which important, data-driven features, such as skewness and multimodality, are allowed. By marginalizing the Polya tree, exact inference is possible up to Markov chain Monte Carlo error.