Asymptotic optimality theory for active quickest detection with unknown postchange parameters

Abstract

The active quickest detection problem with unknown postchange parameters is studied under the sampling control constraint, where there are p local streams in a system but one is only able to take observations from one and only one of these p local streams at each time instant. The objective is to raise a correct alarm as quickly as possible once the change occurs subject to both false alarm and sampling control constraints. Here we assume that exactly one of the p local streams is affected, and the postchange distribution involves unknown parameters. In this context, we propose an efficient greedy cyclic sampling–based quickest detection algorithm and show that our proposed algorithm is asymptotically optimal in the sense of minimizing the detection delay under both false alarm and sampling control constraints. Numerical studies are conducted to show the effectiveness and applicability of the proposed algorithm.

Keywords:

• Active sampling
• asymptotic optimality
• change point detection
• CUSUM

DISCLOSURE STATEMENT

The authors have no conflicts of interest to report.

Additional information

Funding

This work was partially supported by NSF grant DMS-2015405 and the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number UL1TR002378. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.