Tracking Stopping Times Through Noisy Observations

A novel quickest detection setting is proposed, generalizing the well-known Bayesian change-point detection model. Suppose {(Xi,Yi)}i ges 1 is a sequence of pairs of random variables, and that S is a stopping time with respect to {Xi}i ges 1. The problem is to find a stopping time T with respect to {Yi}i ges 1 that optimally tracks S, in the sense that T minimizes the expected reaction delay BBE (T-S)⁺, while keeping the false-alarm probability P(T<S) E(T-S) below a given threshold alpha isin [0,1]. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control.