Date of Award

Spring 5-2018

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Master of Arts (AM/MA)

Degree Type

Thesis

Abstract

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.

Language

English (en)

Chair and Committee

Todd Kuffner

Committee Members

Jimin Ding, José E. Figueroa-López

Comments

Permanent URL: https://doi.org/10.7936/K70Z72R7

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