I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize “my” Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are!

I have to admit that my own Bayesian views and practices have changed. In particular, I resonate with Senn’s point that conventional flat priors miss a lot and that Bayesian inference can work better when real prior information is used. Here I’m not talking about a subjective prior that is meant to express a personal belief but rather a distribution that represents a summary of prior scientific knowledge. Such an expression can only be approximate (as, indeed, assumptions such as logistic regressions, additive treatment effects, and all the rest, are only approximations too), and I agree with Senn that it would be rash to let philosophical foundations be a justification for using Bayesian methods. Rather, my work on the philosophy of statistics is intended to demonstrate how Bayesian inference can fit into a falsificationist philosophy that I am comfortable with on general grounds.

Which among I. J. Good’s 46,656 varieties of Bayesian are you?

I think that this business of pointing to zillions of varieties is just a cop-out that allows some people to say, whatever I do, it’s Bayesian deep down (BADD), or it has Bayesian grounding . There has to be something that counts as not-X for the claim of holding X to have any merit. It’s not that it matters which account is getting credit, whatever that means. It’s that failing to be very clear on the underlying foundations creates an obstacle to doing things better, or to even understanding what the criteria should be for using a given method for a certain problem, or so I think.

Of course, I’m no kind of Bayesian, but rather an error statistical philosopher.

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