Asymptotic analysis of Bayesian quickest change detection procedures

In the sixties, Shiryaev obtained the structure of the optimal quickest change detection procedure for detecting changes in i.i.d. sequences in a Bayesian setting. However, the analysis of the performance of this procedure in terms of average detection delay versus false alarm probability has been an open problem. In this paper, we investigate the performance of the optimal Bayesian quickest change detection procedure in an asymptotic setting where the false alarm probability goes to zero. The results of this study are shown to be especially important in deriving asymptotically optimal solutions to decentralized quickest change detection problems.