On the Bayesian Sequential Change-Point Detection

Abstract

. The problems of sequential change-point have several important appli-cations, including quality control, failure detection in industrial, finance and signal detection. We discuss a Bayesian approach in the context of statistical process control: at an unknown time (cid:28) , the process behavior changes and the distribution of the data changes from p 0 to p 1 . Two cases are considered: (i) p 0 and p 1 are fully known, (ii) p 0 and p 1 belong to the same family of distributions with some unknown parameters (cid:18) 1 , (cid:18) 2 . We present a maximum a posteriori estimate of the change-point which, for the case (i) can be computed in a sequential manner. In addition, we propose the use of the Shiryaev’s loss function. Under this assumption, we define a Bayesian stopping rule. For the Poisson distribution and in the two cases (i) and (ii), we obtain results for the conjugate prior.