Measuring Bayesian Robustness Using Rényi's Divergence and Relationship with Prior-Data Conflict
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This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighbourhood of the elicited prior are considered. The first one is the well-known ϵ-contaminated class, while the second one is the geometric mixing class. The proposed measure of robustness is based on computing the curvature of Rényi's divergence between posterior distributions. The relationship between robustness and prior data conflict has been studied. Through two examples, a strong connection between robustness and prior-data conflict has been found.
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