Comment on “confidence, credibility and prediction”
The historical review of confidence and credibility intervals that begins this article seems to me generally to ring true. The main body of the paper concerns the relationship between confidence and credibility intervals, viewed from frequentist and Bayesian perspectives, and the assessment of Bayesian prediction intervals. I part company with the authors on these topics, for reasons that I now describe, using quotes from the article as stepping-off points.
1. “For Bayesians …why should the choice of prior be determined by the frequentist coverage of the credible interval?”
I would not go so far as to say “determined” by frequentist coverage, but I would say that good frequentist properties are an important goal of a good inference. The Achilles heel of the Bayesian paradigm is that a terrible Bayesian model can yield a terrible answer—the fact that it is “coherent” does not mean that it is necessarily any good.
All statisticians, frequentist or Bayesian, should seek to be well...