A NOTE ON BOUNDED INFLUENCE IN BAYESIAN-ANALYSIS

Let x be a single observation from a distribution having unknown locat ion parameter theta. Dawid (1973) provided sufficient conditions for t he posterior distribution of theta to approach the prior distribution as x tends to infinity, so that an outlier has bounded and vanishing i nfluence on the posterior distribution. We present a result closely re lated to Dawid's theorem. This enables us to consider priors and likel ihoods for the location problem which have bounded but nonvanishing in fluence on posterior moments. Examples are given.