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.