Density based classes of priors: Infinitesimal properties and approximations

We define a notion of local sensitivity for classes of prior densities. The local sensitivity measures how much a small change in the prior affects the posterior. We find an explicit expression for this local sensitivity and we use it as a diagnostic for robustness. We also show that the local sensitivity can be used to find simple, accurate approximations to upper and lower bounds of posterior expectations. © 1995.