Computational Bayesian methods applied to complex problems in bio and astro statistics.

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 simulation to analyze how estimates of a parameter of interest change across sample sizes.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2019

Author dc:creator

• Elrod, Chris Michael, 1991-

Advisor dc:contributor.advisor

• Hejduk, Matthew Dickerson, 1967-

• TBD.
• Bayesian Normal-Inverse-Wishart model.
• Bayesian methods.
• Hamiltonian Monte Carlo.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/10803

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/10803