Quickest Search for a Change Point

Abstract

This paper considers a sequence of random variables generated according to a common distribution. The distribution might undergo periods of transient changes at an unknown set of time instants, referred to as change-points. The objective is to sequentially collect measurements from the sequence and design a dynamic decision rule for the quickest identification of one change-point in real time, while, in parallel, the rate of false alarms is controlled. This setting is different from the conventional change-point detection settings in which there exists at most one change-point that can be either persistent or transient. The problem is considered under the minimax setting with a constraint on the false alarm rate before the first change occurs. It is proved that the Shewhart test achieves exact optimality under worst-case change points and also worst-case data realization. Numerical evaluations are also provided to assess the performance of the decision rule characterized.

Optimal sequential decision rule for cooperative spectrum sensing of CUAVNs

“…T. S. Lau and W. P. Tay in Reference 29 proposed the window‐limited simplified generalized likelihood ratio (LRT) stopping time to quickly detect the critical change without needing increasing computational resources as the sensing samples increases. In Reference 11, J. Heydari and A. Tajer analyzed the quickest search problem for transient change‐points in order to detect one of the change‐points subject to a hard detection delay constraint. X. Ma et al formulated the Bayesian two‐stage sequential change diagnosis problem in Reference 19 to obtain the optimal rule.…”