A Quasi-Bayesian change point detection with exchangeable weights

Abstract

A Quasi-Bayesian change point test statistic is derived, under the fixed and random exchangeable priors, which is asymptotically close to an important subclass of Poisson–Dirichlet weights. While detecting change at each point, the random prior can be updated for future change points in a sequential sampling manner. Asymptotic behaviors of quasi-Bayesian test statistics, under the null and alternative hypothesis are represented in terms of stochastic integrals. Also, the M-estimate approaches for change in mean for both cases of finite and infinite variance observations are discussed. Aside to the application in change point detections, the asymptotic analysis reveals some interesting probabilistic properties. Multiple change point detection and simulation of finite sample distribution of test statistics are studied Finally, a conclusion section is also given.