Degree Type

Dissertation

Date of Award

2017

Degree Name

Doctor of Philosophy

Department

Statistics

Major

Statistics

First Advisor

Daniel J. Nordman

Second Advisor

Stephen B. Vardeman

Abstract

Markov chain Monte Carlo (MCMC) is a computational statistical approach for numerically approximating distributional quantities useful for inference that might otherwise be intractable to directly calculate. A challenge with MCMC methods is developing implementations which are both statistically rigorous and computationally scalable to large data sets. This work generally aims to bridge these aspects by exploiting conditional independence, or Markov structures, in data models. Chapter 2 investigates the model properties and Bayesian fitting of a graph model with Markovian dependence used in deep machine learning and image classification, called a restricted Bolzmann machine (RBM), and Chapter 3 presents a framework for describing inherent instability in a general class of models which includes RBMs. Chapters 4 and 5 introduce a fast method for simulating data from a Markov Random Field (MRF) by exploiting conditional independence specified in the model and a flexible `R` package that implements the approach in C++.

DOI

https://doi.org/10.31274/etd-180810-5163

Copyright Owner

Andrea Kaplan

Language

en

File Format

application/pdf

File Size

127 pages

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