Density Estimation Using Nonparametric Bayesian Methods
Yanyi Wang · Open Scholarship Institutional Repository (Washington University in St. Louis) · 2018
In modern data analysis, nonparametric Bayesian methods have become increasingly popular. These methods can solve many important statistical inference problems, such as density estimation, regression and survival analysis. In this thesis, We utilize several nonparametric Bayesian methods for density estimation. In particular, we use mixtures of Dirichlet processes (MDP) and mixtures of Polya trees (MPT) priors to perform Bayesian density estimation based on simulated data. The target density is a mixture of normal distributions, which makes the estimation problem non-trivial. The performance of these methods with frequentist nonparametric kernel density estimators is assessed according to a mean-square error criterion. For the cases we consider, the nonparametric Bayesian methods outperform their frequentist counterpart.