A Bayesian analysis of a change in the mean of independent normal sequence with contaminated observation

Abstract

In this paper, we consider a Bayesian analysis of a change in the mean of independent gaussian samples in the presence of a single outlier. An unconditional Bayesian significance test for testing change versus no change is performed under consideration of non informative prior distribution of the parameters. From a numerical study using the Gibbs sampler algorithm, the effect of a contaminated observation on the performance of the Bayesian significance test of change is studied. Keywords: Gaussian models; Change-point; HPD region sets; p-value; Outliers. AMS 2010 Mathematics Subject Classification Objects: 91B84; 62F15; 62F03