Detecting changes in a Poisson process monitored at random time intervals

ABSTRACT

We look at a Poisson process where the arrival rate changes at some unknown time point. We monitor this process only at certain time points. At each time point, we count the number of arrivals that happened in that time interval. In previous work, it was assumed that the time intervals were fixed in advance. We relax this assumption to assume that the time intervals in which the process are monitored is also random. 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 then compare various observation schemes to determine the best model. We provide some numerical results to illustrate the effectiveness of the detection procedures.

KEYWORDS:

• Bayesian stopping rules
• change-point detection
• dynamic programming
• Poisson processes
• randomized processes
• risk

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62L15
• 60G40

Acknowledgments

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