A Consistent On-Line Bayesian Procedure For Detecting Change Points

Bayesian inference on the change points in a given sample is a statistical model selection problem that presents two main difficulties. The first one is the selection of a reasonable prior distribution over the set of models, the number of which depends exponentially on the sample size, and the second is the high computational burden involved even when Markov chain Monte Carlo methods are used.We consider normal linear sampling models for describing the data between consecutive change points, the hierarchical uniform prior over the set of models, intrinsic priors over their model parameters, and to discuss an on-line Bayesian procedure that alleviates the computational burden for moderate or large sample sizes. Under wide conditions, this procedure is shown to be consistent. Illustrations on simulated and real data sets are given, including the analysis of the change points in the annual mean temperature in central England for the years 1659 to 2011. Copyright (C) 2013 JohnWiley & Sons, Ltd.