Author

Erina Paul

Publication Date

2017

Document Type

Dissertation/Thesis

First Advisor

Basu, Sanjib

Degree Name

Ph.D. (Doctor of Philosophy)

Department

Department of Mathematical Sciences

LCSH

Mathematics||Statistics

Abstract

Many scientific problems require statistical inference in complex models. Bayesian nonparametric models provide a flexible modeling and inference framework for such problems. There is a substantial literature on Bayesian computational methods for nonparametric models, however, in non-conjugate complex models, they can be difficult or computationally expensive to implement. Approximate Bayesian Computation (ABC) provides a computational framework for inference in difficult and intractable Bayesian models. The idea behind ABC is to provide an approximate posterior inference without evaluating the likelihood function based on samples drawn from the sampling distribution. We develop a methodology for statistical inference in nonparametric Bayesian models based on ABC. We utilize the conditionally independent model structure to address the difficult problem of summary statistic choice in ABC. The developed method is generalized to complex nonlinear Bayesian nonparametric models, including generalized linear mixed models and survival models for recurrent data. We further generalize this approach to Bayesian nonparametric models involving the Pitman-Yor process. The approach is further extended to Bayesian nonparametric models involving the stable distributions which are often intractable due to lack of closed-form expressions. Throughout this dissertation, we illustrate the proposed methods in simulated and real datasets and we compare their performances with preexisting methods.

Comments

Advisors: Sanjib Basu.||Committee members: Ilya Krishtal; Alan Polansky; Duchwan Ryu; Michelle Xia.||Includes bibliographical references.||Includes illustrations.

Extent

ix, 127 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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