on the bayesian sequential change-point detection

the problems of sequential change-point have several important applications in quality control, signal processing, and failure detection in industry and finance. we discuss a bayesian approach in the context of statistical process control: at an unknown time $tau$, the process behavior changes and the distribution of the data changes from p0 to p1. two cases are considered: (i) p0 and p1 are fully known, (ii) p0 and p1 belong to the same family of distributions with some unknown parameters θ1≠θ2. 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.