SENSITIVITY OF A BAYESIAN-ANALYSIS TO THE PRIOR DISTRIBUTION

Consider the problem of eliciting and specifying a prior probability d istribution for a Bayesian analysis. There will generally be some unce rtainty in the choice of prior, especially when there is little inform ation from which to construct such a distribution, or when there are s everal priors elicited, say, from different experts. It is of interest , then, to characterize the sensitivity of a posterior distribution (o r posterior mean) to prior. We characterize this sensitivity in terms of bounds on the difference between posterior distributions correspond ing to different priors. Further, we illustrate the results on two dis tinct problems: a) determining least-informative (vague) priors and b) estimating statistical quantiles for a problem in analyzing projectil e accuracy.