Dissertation/Thesis Abstract

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics
by Elrod, Chris, Ph.D., Baylor University, 2019, 103; 27540692
Abstract (Summary)

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Indexing (document details)
Advisor: Stamey, James, Hejduk, Matthew
Commitee: Seaman, John, Young, Dean, Ryden, David
School: Baylor University
Department: Statistical Science
School Location: United States -- Texas
Source: DAI-B 81/7(E), Dissertation Abstracts International
Subjects: Statistics
Keywords: Computational Bayesian methods, Complex problems, Bio and astro statistics
Publication Number: 27540692
ISBN: 9781392479230
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