A bayesian decision-theoretic change-point detection for i.p.i.d. sources

Change-point detection is the problem of finding points of time when a probability distribution of samples changed. There are various related problems, such as estimating the number of the changepoints and estimating magnitude of the change. Though various statistical models have been assumed in the field of change-point detection, we particularly deal with i.p.i.d. (independent-piecewise-identically-distributed) sources. In this paper, we formulate the related problems in a general manner based on statistical decision theory. Then we derive optimal estimators for the problems under the Bayes risk principle. We also propose e_cient algorithms for the change-point detection-related problems in the i.p.i.d. sources, while in general, the optimal estimations requires huge amount of calculation in Bayesian setting. Comparison of the proposed algorithm and previous methods are made through numerical examples.