Quickest Detection with Discretely Controlled Observations

Abstract

We study a continuous-time Bayesian quickest detection problem in which observation times are a scarce resource. The agent, limited to making a finite number of discrete observations, must adaptively decide his observation strategy to minimize detection delay and the probability of false alarm. Under two different models of observation rights, we establish the existence of optimal strategies and formulate an algorithmic approach to the problem via jump operators. We describe algorithms for these problems and illustrate them with some numerical results. As the number of observation rights tends to infinity, we also show convergence to the classical continuous observation problem of Shiryaev.

Keywords:

• Bayesian change point detection
• Continuous time
• Finitely many sampling rights

Subject Classifications:

• 62L15
• 60G40
• 62F15

ACKNOWLEDGMENT

We are grateful to the editor Professor Nitis Mukhopadhyay for a very timely handling of our article.

Notes

Recommended by Nitis Mukhopadhyay

Color versions of one or more of the figures in the article can be found online at http://www.tandfonline.com/lsqa.