Detection of Changes in a Multinomial Process

Abstract

We look at a multinomial distribution where the probabilities of landing in each category change at some unknown integer. We assume that the probability structure both before and after the change is known, and the problem is to find the probability that the probability structure has changed. For a loss function consisting of the cost of late detection and a penalty for early stopping, we develop, using dynamic programming, the one and two steps look ahead Bayesian stopping rules. We provide some numerical results to illustrate the effectiveness of the detection procedures. We show that the two step ahead procedure is a slight improvement over the one step ahead procedure. However the two procedures are very consistant in their stopping times.