Sensitivity of a Bayesian analysis to the prior distribution

Consider the problem of eliciting and specifying a prior probability distribution for a Bayesian analysis. There will generally be some uncertainty in the choice of prior, especially when there is little information from which to construct such a distribution, or when there are several priors elicited, say, from different experts. It is of interest, then, to characterize the sensitivity of a posterior distribution (or posterior mean) to prior. We characterize this sensitivity in terms of bounds on the difference between posterior distributions corresponding to different priors. Further, we illustrate the results on two distinct problems: a) determining least-informative (vague) priors and b) estimating statistical quantiles for a problem in analyzing projectile accuracy