I'm afraid you're mistaken -- frequentist statistics are not a special case of Bayesian statistics, and there is generally no "implicit, built-in prior" that al

I'm afraid you're mistaken -- frequentist statistics are not a special case of Bayesian statistics, and there is generally no "implicit, built-in prior" that allows you to get frequentist worst-case guarantees from Bayesian techniques. Consider the case of a confidence interval on a binary proportion given a finite number of samples. A frequentist method will produce an interval that includes the true value of the proportion with at least x% probability, even in the worst case, for any proportion between 0 and 1. (E.g. the Blyth-Still-Casella method or the Clopper-Pearson method.) An x% credible interval will include the true value exactly x% of the time, averaged over all values of the proportion weighted according to the prior. This will not provide the same guarantee (much less the same interval extent!), no matter what prior is used. Which is not to say the credible interval is bad or inappropriate. It's just not the same kind of tool. It is optimizing a different penalty function of non-inclusion. (Another example where the "Bayesian" technique is not quite as conservative as necessary to achieve a frequentist-style guarantee, even with a uniform prior: http://www.quora.com/I-have-burned-200-disks-and-I-want-to-make-sure-that-they-are-all-in-perfect-working-order-What-is-the-smallest-size-sample-I-could-test-in-order-to-be-relatively-confident-that-98-of-all-the-disks-are-fine-burned-correctly?share=1 http://www.quora.com/I-have-burned-200-disks-and-I-want-to-m...)