Frequentist accuracy of Bayesian estimates
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2015 · Volume 77 · Issue 3
Abstract
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. The Bayes rule will still produce nice looking estimates and credible intervals, but these lack the logical force that is attached to experience-based priors and require further justification. The 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 as 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.
Keywords
Approximate bootstrap confidence intervals, General accuracy formula, Hierarchical and empirical Bayes, Markov chain Monte Carlo methods, Parametric bootstrap
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