Professor Donald Martin (North Carolina State University)

Computing probabilities for the discrete scan statistic through slack variables

The discrete scan statistic is used in many areas of applied probability and statistics to study local clumping of patterns.

Testing based on the statistic requires tail probabilities. Whereas the distribution has been studied extensively, most of the results are approximations, due to the difficulties associated with the computation. Results for exact tail probabilities for the statistic have been given for a binary sequence that is independent or first-order Markovian. We give an algorithm to obtain probabilities for the statistic over multi-state trials that are Markovian of a general order of dependence, and explore the algorithm’s usefulness.