Bayesian single change point detection in a sequence of multivariate normal observations

Abstract

A Bayesian method is used to see whether there are changes of mean, covariance, or both at an unknown time point in a sequence of independent multivariate normal observations. Noninformative priors are used for all competing models: no-change model, mean change model, covariance change model, and mean and covariance change model. We use several versions of the intrinsic Bayes factor of Berger and Pericchi (Berger, J.O. and Pericchi, L.R., 1996, The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association,\/ 91, 109–122; Berger, J.O. and Pericchi, L.R., 1998, Accurate and stable Bayesian model selection: the median intrinsic Bayes factor. Sankhya Series B, 60, 1–18.) to detect a change point. We demonstrate our results with some simulated datasets and a real dataset.