Quickest change point detection with sampling right constraints

Abstract

In this paper, quickest detection problem with sample right constraints is considered. Specifically, there is a sequence of samples whose probability density function will change at an unknown time. The goal is to detect such a change in a way that a linear combination of the detection delay and false alarm probability is minimized. However, one can take at most N observations from this random sequence. In this paper, we show that the cost function can be written as a set of iterative functions, which can be solved by optimal Markov stopping theorem. The optimal stopping rule is shown to be a threshold rule. To assist the analysis of the optimal scheme, several schemes whose delay performances bound the delay performance of the optimal scheme are developed. Asymptotic performance analysis indicates that the performance of the quickest detection with sample right constraints is close to that of the classic Bayesian quickest detection for several scenarios of practical interest.