Using Differential Geometry to Study Robustness in Bayesian Statistics

An important problem in Bayesian statistics is how the choice of prior distributions influence inferences. One way to study this is to compare values of measures of distance between prior and posterior distributions for different sample sizes and parameter values. The geodesic distance between probability distributions originally proposed by C.R.Rao is one such measure. Using formulae for the geodesic distances between probability distributions the distances between posterior distributions are obtained for gamma prior distributions and exponential and Poisson populations . Some asymptotic results about these distances are derived.