Frequentist Accuracy of Bayesian Estimates

In the absence of relevant prior experience, popular Bayesian estimation techniques usually begin with some form of "uninformative" prior distribution intended to have minimal inferential influence. Bayes rule will still produce nice-looking estimates and credible intervals, but these lack the logical force attached to experience-based priors and require further justification. This paper concerns the frequentist assessment of Bayes estimates. A simple formula is shown to give the frequentist standard deviation of a Bayesian point estimate. The same simulations required for the point estimate also produce the standard deviation. Exponential family models make the calculations particularly simple, and bring in a connection to the parametric bootstrap.