The behavior of an organism is a set of characters that is just as critical to the understanding of biology as the morphological and physiological features of the individual. Statistically robust description of behavioral processes is, unfortunately, more difficult to obtain than in the more traditional fields of biology. Especially when the task is to indicate the occurrence of subtle behavioral changes, merely counting the number or duration of a behavior pattern is insufficient. Recent applications of Continuous Time Markov Chain (CTMC) models to Ethology have shown great promise as a descriptive and hypothesis-testing tool. Researchers have indicated otherwise undetectable changes of sub-threshold doses of amphetamines and electrical stimulation of the brain. Unfortunately, many of the statistical techniques available are poorly suited for fitting CTMC models to behavior for a variety of reasons such as high alpha error rates, inability to deal with normally encountered sample sizes, number of ties and censored observations, and the need to have computationally simple solutions that can be used as standard PC-based routines. This project will consider the design and implementation of generalizations of the CTMC model. In particular, while the transition times in such models usually follow simple exponential distributions, this project will examine the possibility that these times follow a distribution with nonconstant, piecewise-constant hazard rates. The goal is to create computationally efficient, unbiased, robust statistical techniques to fit such models, paying special attention to estimation of, and inference on, the time or times when the hazard rate changes. These techniques will then be evaluated by testing them on both actual and simulated data sets.
