Detection of Changes of Multiple Poisson Processes Monitored at Discrete Time Points Where the Arrival Rates are Unknown

Abstract

We observe a Poisson process in several categories where the arrival rates in each category change at some unknown integer. For some of these categories the arrival rates increase, whereas in other categores the arrival rates decrease. The point at which the process changes may be different for each category. We assume that both the arrival rates for each category as well as the change-point are unknown. We develop procedures for detecting when a change has occurred in at least one of these categories. We provide some numerical results to illustrate the effectiveness of the detection procedures.

Keywords:

• Bayesian stopping rules
• Change-point detection
• Dynamic programming
• Multiple categories
• Poisson processes
• Risk

Subject Classification:

• 62L15
• 60G40

ACKNOWLEDGMENTS

I would also like to thank the Editor, Associate Editor, and numerous referees for their helpful suggestions. Those suggestions have improved the quality of this article.

Notes

Recommended by Michael Baron