Geodesic
A Bayesian significance test of change for correlated observations
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 51-62

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This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.
Keywords: autoregressive model, change point, HPD region sets, p-value, Gibbs sampler 
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Slama, Abdeldjalil. A Bayesian significance test of change for correlated observations. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 51-62. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a3/