Bayesian Multiple Change-Points Detection in a Normal Model with Heterogeneous Variances

This study considers the problem of multiple change-points detection. For this problem, we develop an objective Bayesian multiple change-points detection procedure in a normal model with heterogeneous variances. Our Bayesian procedure is based on a combination of binary segmentation and the idea of the screening and ranking algorithm (Niu and Zhang in Ann Appl Stat 6:1306–1326, 2012). Using the screening and ranking algorithm, we can overcome the drawbacks of binary segmentation, as it cannot detect a small segment of structural change in the middle of a large segment or segments of structural changes with small jump magnitude. We propose a detection procedure based on a Bayesian model selection procedure to address this problem in which no subjective input is considered. We construct intrinsic priors for which the Bayes factors and model selection probabilities are well defined. We find that for large sample sizes, our method based on Bayes factors with intrinsic priors is consistent. Moreover, we compare the behavior of the proposed multiple change-points detection procedure with existing methods through a simulation study and two real data examples.