## Don Fraser’s rejoinder

“How can a discipline, central to science and to critical thinking, have two methodologies, two logics, two approaches that frequently give substantially different answers to the same problems. Any astute person from outside would say “Why don’t they put their house in order?”” Don Fraser

Following the discussions of his Statistical Science paper Is Bayes posterior just quick and dirty confidence?, by Kesar Singh and Minge Xie, Larry Wasserman (who coined the neologism Frasian for the occasion), Tong Zhang, and myself, Don Fraser has written his rejoinder to the discussion (although in Biometrika style it is for Statistical Science!). His conclusion that “no one argued that the use of the conditional probability lemma with an imaginary input had powers beyond confidence, supernatural powers” is difficult to escape, as I would not dream of promoting a super-Bayes jumping to the rescue of bystanders misled by evil frequentists!!! More seriously, this rejoinder makes me reflect on lectures from the past years, from those on the diverse notions of probability (Jeffreys, Keynes, von Mises, and Burdzy) to those on scientific discovery (mostly Seber‘s, and the promising Error and Inference by Mayo and Spanos I just received).

### 2 Responses to “Don Fraser’s rejoinder”

1. Fraser criticizes Bayesian probability over and over for not being relative frequency without ever seeming to realize that Bayesians don’t approach probability on that basis but rather use it as a measure of the plausibility of a given proposition. I wish he’d grappled with (or at least mentioned) some of the justifications for the Bayesian approach such as de Finetti’s coherence argument, Cox’s theorem, or Wald’s complete class theorem.

2. I can measure an elephant by its length, weight, or volume. These are three different, yet related, measures, all of them useful in their context. All three tell us the elephant is BIG.

People can infinitely look for equivalences and differences among statistical schools. But, as a practitioner (a quantiative geneticist) I can tell that, in our field, pragmatism is king for choosing tools, and rarely conclusions do differ using one method or the other.

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