Robust Bayesian analysis using divergence measures

We consider the problem of measuring Bayesian robustness of classes of contaminated priors. Two classes of priors in the neighborhood of the elicited prior are considered, one is the usual [var epsilon]-contaminated class and the other one is a geometric mixing class. A global measure, using [phi]-divergence of the posterior distributions and its curvature, is introduced. Calculation of ranges of the curvatures are demonstrated through examples. It is shown that the curvature formulas give unified answers irrespective of the choice of the [phi]-functions. It is also observed that the variation of the posterior divergence measures and their curvature are especially useful for multidimensional problems.