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Generalizations of the statistical flowgraph model framework


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/11196

Generalizations of the statistical flowgraph model framework

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dc.contributor.author Warr, Richard
dc.date.accessioned 2010-09-10T20:17:37Z
dc.date.available 2010-09-10T20:17:37Z
dc.date.issued 2010-09-10
dc.date.submitted July 2010
dc.identifier.uri http://hdl.handle.net/1928/11196
dc.description.abstract Statistical flowgraphs model multistate semi-Markov processes and provide a way to perform inference for these processes. This methodology provides powerful results that significantly impact the study of multistate semi-Markov processes. This dissertation extends previous work in several ways. First, by demonstrating how any "smooth" transition distribution can be incorporated into a statistical flowgraph model (SFGM), we provide a method to use popular distributions, such as the lognormal, that have not been used in the past. Next, we propose an alternate way to consider Bayesian SFGMs by showing how computation can be accomplished when the traditional methods of SFGMs fail to be computationally feasible. We demonstrate this method with a Bayesian non-parametric example. We extend flowgraph models to handle time-varying covariates using an accelerated failure time model. We also show how SFGMs can be used to make inference in multistate semi-Markov models to calculate exact likelihood functions when faced with incomplete data. Finally, we develop a goodness-of-fit criterion that is applicable to any continuous model and can be applied to SFGMs. This goodness-of-fit test criterion is general enough to be useful when dealing with censored and incomplete multistate data. en_US
dc.description.sponsorship United States Air Force en_US
dc.language.iso en en_US
dc.subject Semi-Markov en_US
dc.subject Flowgraph Models en_US
dc.subject Bayesian Statistics en_US
dc.subject Survival Analysis en_US
dc.subject Reliability en_US
dc.subject.lcsh Flowgraphs.
dc.subject.lcsh Markov processes--Mathematical models.
dc.subject.lcsh Lognormal distribution.
dc.subject.lcsh Bayesian statistical decision theory.
dc.subject.lcsh Failure time data analysis.
dc.subject.lcsh Goodness-of-fit tests.
dc.title Generalizations of the statistical flowgraph model framework en_US
dc.type Dissertation en_US
dc.description.degree Statistics en_US
dc.description.level Doctoral en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Christensen, Ronald
dc.description.committee-member Huzurbazar, Aparna
dc.description.committee-member Huerta, Gabriel
dc.description.committee-member Storlie, Curtis

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