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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb
A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb
Theses and Dissertations
Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use …
Spectral Analysis Of Randomly Generated Networks With Prescribed Degree Sequences, Clifford Davis Gaddy
Spectral Analysis Of Randomly Generated Networks With Prescribed Degree Sequences, Clifford Davis Gaddy
Theses and Dissertations
Network science attempts to capture real-world phenomenon through mathematical models. The underlying model of a network relies on a mathematical structure called a graph. Having seen its early beginnings in the 1950's, the field has seen a surge of interest over the last two decades, attracting interest from a range of scientists including computer scientists, sociologists, biologists, physicists, and mathematicians. The field requires a delicate interplay between real-world modeling and theory, as it must develop accurate probabilistic models and then study these models from a mathematical perspective. In my thesis, we undertake a project involving computer programming in which we …