Bayesian robustness in change point analysis

This paper focuses on robustness analysis of non-exchangeable product partition models (PPM), which are widely used to detect multiple change points. Bayesian robustness is usually concerned with the impact of perturbations in prior distributions on posterior inferences. Our contribution is twofold since we consider multiplicative perturbations in the data distribution, as well as in the prior distribution of its parameters. As a novelty in the robust Bayesian and PPM literature, we introduce some sensitivity measures to examine how such perturbations affect the posterior inference on the number of clusters and their location, as well as the product estimates. We focus our analysis on the skew-normal class of distributions, thus building a PPM under skew-normality. We apply the proposed PPM to analyze a Brazilian tomato price data set.