Bayesian change-point estimation in the presence of a single outlier

Abstract

The Bayesian estimation of the change-point in independent gaussian samples is considered. The impact of an outlier on the performance of the Bayesian procedure is studied and the posterior density under contamination is given. In this paper, we show that, in the case of small samples, an outlier has a significant impact on the estimation of the change-point. However, if the sample size is enough high, the estimation performs well.