Bayesian semiparametric regression models with mixtures of constrained Polya Tree priors.

Abstract

It has become more and more evident that under many circumstances assumptions used in parametric analysis about underlying populations from which the data are obtained are very restrictive. As more flexible methods than parametric approach, Bayesian nonparametric methods, such as Dirichlet Process and Polya Tree Priors, gained increasing popularity in applications in past few decades. Polya Trees have many good properties such as they are tractable and give probability one to absolutely continuous distributions. In applying Polya Tree priors for the error distribution in semiparametric regressions, moment constraints such as zero mean and (or) unit variance are required to identify the models. In my dissertation, I develop methodological and computational machinery of constrained Polya Tree priors. It is shown that constrained Polya Tree priors can put moment constraints on continuous and bound distributions of various shapes, such as distributions of multiple modes, skewness, etc. I intent to implement this method under various settings of statistical modelling, such as multivariate linear regression, survival models (or duration models), and discrete choice models. The simulation studies and applications on real data sets show that these semiparametric models lead to accurate parameter estimates and the estimated densities using constrained Polya Trees can incorporate data-driven features.