Detection of Changes of a Multinomial Process Where the Probability Structure Before and After the Change Is Unknown

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 unknown, 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-step look-ahead Bayesian stopping rules. We provide some numerical results to illustrate the effectiveness of the detection procedures.

Keywords:

• Bayesian
• Change-point detection
• Dynamic programming
• Multinomial
• Risk
• Stopping rules

Subject Classifications:

• 62L15
• 60G40

ACKNOWLEDGMENTS

I want to thank the Editor, Associate Editor, and referees for their suggestions in preparing this article.

Notes

Recommended by N. Mukhopadhyay