Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Statistics and Data Science

First Advisor

Chang, Joseph

Abstract

With continuing rapid developments in computational power, Bayesian statistical methods, because of their user-friendliness and estimation capabilities, have become increasingly popular in a considerable variety of application fields. In this thesis, applied Bayesian methodological topics and empirical examples focusing on nonhomogeneous hidden Markov models (NHMMs) and measurement error models are explored in three chapters. In the first chapter, a subsequence-based variational Bayesian inference framework for NHMMs is proposed in order to address the computational problems encountered when analyzing datasets containing long sequences. The second chapter concentrates on measurement error models, where a Bayesian estimation procedure is proposed for the partial potential impact fraction (pPIF) with the presence of measurement error. The third chapter focuses on an empirical application in marketing, where a coupled nonhomogeneous hidden Markov model (CNHMM) is introduced to provide a novel framework for customer relationship management.

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