Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD.


Due to the versatility of its structure, the semi-Markov process is a powerful modeling tool used to describe complex systems. Though similar in structure to continuous time Markov chains, semi-Markov processes allow for any transition time distribution which enables these processes to t a wider range of problems than the continuous time Markov chain. While semi-Markov processes have been applied in fields as varied as biostatistics and finance, there does not exist a theoretically-based, systematic method to determine if a semi-Markov process accurately fits the underlying data used to create the model. In fields such as regression and analysis of variance, the quality of the predictive model is judged in part by the goodness of fit of the model which relates the expected observation values with the actual observations. A similar methodology for semi-Markov processes would provide immediate insight in the efficacy of the fitted model and would allow competing models to be directly compared with one another. This dissertation presents a methodology to measure the adequacy of a fitted semi-Markov process. To this end, a technique to assess the likelihood that a data sample could be generated by a specific semi-Markov process is developed, including a newly proposed goodness of fit metric. This technique relies on the covariance structure of the semi-Markov process; thus, a method to estimate the covariance structure is also proposed. The technique is applied to real and simulated data to demonstrate the goodness of fit metric's utility in model validation and its ability to identify potential covariate factors within the model.

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