The Distribution of Pattern Counts in Markov Chains With Stopping Rules: With Application to Behavioral Teratology Experiments
Francis C. Hsuan, Milton N. Parnes, Thomas E. Bradstreet · Statistics in Biopharmaceutical Research · 2009
We consider a logistic transition model for analyzing strings of correlated binary (0,1) data, which occur in behavioral teratology experiments targeted at testing learning impairment in rat pups. Estimating the learning parameter in the model has led us to the following question: How to find the joint distribution of the counts of overlapping occurrences of {00}, {01}, {10}, and {11} in a string, when the string is ended when k, k>2, successes in a row are observed? Similar questions have been tackled in the literature using a variety of methods. Here, we use Markov potential theory to find the joint moment generating function, and derive an explicit formula for the joint probability distribution. This result is then used to find the asymptotic standard error of a consistent estimator for the learning parameter in the logistic transition model. We illustrate our results with a real behavioral teratology dataset.