I just noticed Andrew Gelman’s blog today. ..too good to let pass without quick comment: He asks:

What is a Bayesian?

Deborah Mayo recommended that I consider coming up with a new name for the statistical methods that I used, given that the term “Bayesian” has all sorts of associations that I dislike (as discussed, for example, in section 1 of this article).

I replied that I agree on Bayesian, I never liked the term and always wanted something better, but I couldn’t think of any convenient alternative. Also, I was finding that Bayesians (even the Bayesians I disagreed with) were reading my research articles, while non-Bayesians were simply ignoring them. So I thought it was best to identify with, and communicate with, those people who were willing to engage with me.

More formally, I’m happy defining “Bayesian” as “using inference from the posterior distribution, p(theta|y)”. This says nothing about where the probability distributions come from (thus, no requirement to be “subjective” or “objective”) and it says nothing about the models (thus, no requirement to use the discrete models that have been favored by the Bayesian model selection crew). Based on my minimal definition, I’m as Bayesian as anyone else.

He may be “as Bayesian as anyone else,” but does he really want to be as Bayesian as anyone? (slight, deliberate equivocation). As a good Popperian, I concur (with Popper), that names should not matter, but Gelman’s remarks suggest he should distinguish himself, at least philosophically[i].

As in note [iv] of my Wasserman deconstruction: “Even where Bayesian methods are usefully applied, some say ‘most of the standard philosophy of Bayes is wrong’ (Gelman and Shalizi 2012, 2 n2)”.

In the paper Gelman today cites (from our RMM collection):

… we see science—and applied statistics—as resolving anomalies via the creation of improved models which of- ten include their predecessors as special cases. This view corresponds closely to the error-statistics idea of Mayo (1996). (Gelman 2011, 70)

If the foundations for these methods are error statistical, then shouldn’t that come out in the description? (error-statistical Bayes?) It seems sufficiently novel to warrant some greater gesture, than ‘this too is Bayesian’.)

In that spirit I ended my deconstruction with the passage:

Ironically many seem prepared to allow that Bayesianism still gets it right for epistemology, even as statistical practice calls for methods more closely aligned with frequentist principles. What I would like the reader to consider is that what is right for epistemology is also what is right for statistical learning in practice. That is, statistical inference in practice deserves its own epistemology. (Mayo, 2011p. 100)

What do people think?

[i] To Gelman’s credit, he is one of the few contemporary statisticians to (openly) recognize the potential value of philosophy of statistics for statistical *practice*!