Another intriguing point for the discussion.

Jaynes cites Zellner and Thornber's experiments comparing the performance of Bayesian vs frequentist methods. Bayes won in both cases, I presume on coverage too. The reason for that was pretty funny: quote, "By the time all necessary provisions for a 'fair' contest have been incorporated into the experiment, all the ingredients of the Bayesian theory (prior distribution, loss function, etc.) will necessarily be present... The simulation can only demonstrate the mathematical theorem." In other words, frequentist confidence coverage might sometimes win on real-world examples like the Avogadro number, but Bayes will win any arranged contests precisely because they're arranged. :-)

To those who feel anti-Bayesian today I recommend Shalizi's blog, and also the following joke I found on the net:

Prior to the birth of Thomas Bayes, the proud parents, Mr Joshua Bayes and Mrs. Ann Carpenter Bayes, had 11 daughters (Anne, Rebecca, Mary, etc). While Mrs. Bayes was pregnant with Thomas, she REALLY, REALLY wanted a son. So they went to the local seer, who placed her hands on Mrs. Bayes' stomach and pronounced that without a doubt, the next baby would be a boy. Well, Mrs. Bayes really, really believed that this next baby would be a boy. So when the baby actually arrived, the actual physical evidence that the baby was a girl was not strong enough to overcome her prior (ahem) belief that the baby would be a boy, and so Joshua and Anne named their new baby daughter Thomas and raised her to be the son they had always wanted.