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 of this model to discover disease and treatment topics in a corpus of health insurance claims data. By representing individuals as mixtures of topics, we are able to consider their future costs on an individual level rather than as part of a large collective.
Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-4804 |
Date | 18 October 2013 |
Creators | Webb, Jared Anthony |
Publisher | BYU ScholarsArchive |
Source Sets | Brigham Young University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations |
Rights | http://lib.byu.edu/about/copyright/ |
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