%0 Journal Article
%A Gholami, Gholamhossein
%T On the Bayesian Sequential Change-Point Detection
%J Journal of the Iranian Statistical Society
%V 16
%N 1
%U http://jirss.irstat.ir/article-1-381-en.html
%D 2017
%K Bayesian Sopping Rule, Change-Point Detection, Maximum a Posteriori Estimation, Sequential Bayesian Analysis, Shiryaevâ€™s Loss Function.,
%X 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.
%> http://jirss.irstat.ir/article-1-381-en.
%P 77-94
%& 77
%!
%9 Original Paper
%L A-11-370-2
%+ Department of Mathematics, Faculty of Sciences, Urmia University, Iran
%G eng
%@ 1726-4057
%[ 2017