Fatherly advice is pretty heavy stuff. Am I being presumptuous in offering advice under such a pretence? Perhaps I should state my credentials. This, of course, would be an unusual tactic, since the traditional approach at this point would be to mush on with one’s conclusions and leave it to the book’s reviewers to judge the strength of the case for people reading what you have to say and for taking it seriously. I believe the book largely makes its own case. So I won’t bore you with a list of accomplishments or awards that might appear to give me an air of authority. Instead, I’d say that my main qualification for offering fatherly advice is that I am old. Older people tend to accumulate information and insights that younger people might not yet have gotten to. My own journey in the field of Statistics includes an evolving appreciation for Bayesian methods, in spite of an ever-present skepticism about the appropriateness of their universal applicability. But for quite a long time, the question of “when“ one should be a Bayesian seemed to me to be quite elusive. The formulation of the comparative performance of Bayesian and frequentist procedures as a “threshold problem,“ with performance measured relative to the “true state of nature,“ provided (for me, at least) some interesting inroads into the answer to this vexing question. Having explored various versions of this and closely related problems over the last twenty years, I believe that I really do have some fatherly advice to share.
KeywordsPrior Distribution Frequentist Estimator Target Parameter Bayesian Treatment Threshold Problem
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