TY - JOUR
T1 - On the Bayesian Sequential Change-Point Detection
JF - JIRSS
JO - JIRSS
VL - 16
IS - 1
UR - http://jirss.irstat.ir/article-1-381-en.html
Y1 - 2017
SP - 77
EP - 94
KW Bayesian Sopping Rule
KW Change-Point Detection
KW Maximum a Posteriori Estimation
KW Sequential Bayesian Analysis
KW Shiryaevâ€™s Loss Function.
N2 - 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.
M3 10.18869/acadpub.jirss/20170601
ER -