Physical Sciences and Mathematics Commons^™

Bayesian Topological Machine Learning, Christopher A. Oballe

Doctoral Dissertations

Topological data analysis encompasses a broad set of ideas and techniques that address 1) how to rigorously define and summarize the shape of data, and 2) use these constructs for inference. This dissertation addresses the second problem by developing new inferential tools for topological data analysis and applying them to solve real-world data problems. First, a Bayesian framework to approximate probability distributions of persistence diagrams is established. The key insight underpinning this framework is that persistence diagrams may be viewed as Poisson point processes with prior intensities. With this assumption in hand, one may compute posterior intensities by adopting techniques …

Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey

Mathematics & Statistics ETDs

Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive …

On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams

Graduate College Dissertations and Theses

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics.

This body of work first explores the role of strain-transcending immunity in mathematical disease models, …