I just discovered a written comment, actually two, on my sketch-paper “The Third Way Of Probability & Statistics: Beyond Testing and Estimation To Importance, Relevance, and Skill“. Now when I say “I” I mean not I, but reader Bill Raynor. He directs us to the blog of Christian Robert, which I hadn’t known even existed.
Robert’s first comments ran along these lines (ellipses original):
[T]he document somewhat sounds like a practical (?) joke. And almost made me wonder whether Mr Briggs was a pseudonym…And where the filter behind arXiv publishing principles was that day.
The notion behind Briggs’ third way is that parameters do not exist and that only conditional probability exists. Not exactly a novel perspective then. The first five pages go on repeating this principle in various ways, without ever embarking into the implementation of the idea, at best referring to a future book in search of a friendly publisher…The remainder of the paper proceeds to analyse a college GPA dataset without ever explaining how the predictive distribution was constructed. The only discussion is about devising a tool to compare predictors, which is chosen as the continuous rank probability score of Gneiting and Raftery (2007). Looking at those scores seems to encompass this third way advocated by the author, then, which sounds to me to be an awfully short lane into statistics. With no foray whatsoever into probability.
Well, if “Mr Briggs” is a pseudonym don’t expect me to cop to it at this late date. I find it amusing Robert would have had Arxiv censor the paper. This is in accord with the best modern-day scientific practice of locking out the opposition.
Anyway, parameters don’t exist. If you think they do, find me one. I’ll wait here. Better, send me one in the mail. I’ll pay shipping. (I’m nothing if not generous. Incidentally, statisticians scarcely think about the origin of parameters.) Robert misreads me: I do not say “only conditional probability exists.” I say no probability of any kind exists. I say all probability is conditional; I also say all probability is epistemological. It’s true this is not a “novel perspective,” but my view does has the benefit of being true. I’ll take truth over novelty any day.
Incidentally, I have found a friendly publisher, as regular readers know. It was impossible in the sketch-paper to do more than sketch, which is why I refer to the book. I’ll let Robert know when it’s out.
How I derived the predictive distribution for the GPA example I thought too trivial to mention. It’s the standard, out-of-the-box Bayesian posterior predictive distribution for linear regression (which I referenced). And anyway, I have no particular love for that model. Use any model you like. I also don’t advocate the CRPS above all other scores. Indeed, as I insist, use the score that accords with the decisions you make with the probability model. Different people will thus—rightly—come to different views of the same model. Just like real life, eh?
The only real objection I have is Roberts’s last comment: “With no foray whatsoever into probability.” Brother, the exact opposite is true. My approach (old and not novel) is strict or pure probability. There’s no statistics to it, where by “statistics” I mean the ad hoc decision rules and other extra-probability procedures (Bayes or frequentist) used in the field. Instead of opaque models married to ritual, the “third way” emphasizes nothing but verifiable probabilities of observables, in which decision is identified as not probability, as it should be.
Somebody calling himself “coreyyanofsky” had this to say to Roberts’s post:
Briggs is an odd duck. His viewpoint, as near as I can tell, is a melding of Jaynes-Cox foundations and a kind of de-Finetti/Theodore-Geisser-style emphasis on predictive inference. I think he thinks that only observable quantities “deserve” to get probability distributions.
I object to the term “odd duck.” That’s odd drake, fella. I will plead guilty to plotting from the Duke & Drake to overthrow the old ways of doing statistics, though.
The rest of the comment is accurate, and even though Theodore Geisser is almost the right name, perhaps Theodor Geisel is more appropriate. I even approve of the scare quotes around “deserve” (as will be clear from my remarks above).
I mentioned two comments by Robert. The second came in a recent talk he gave (in slides 8 and 9). In slide 8, after inappropriately putting scare quotes around the word true, he mentions posterior predictive methods, which is good (though I don’t advocate Gelman’s use of Bayesian posterior p-values).
On slide 9, after sliding back in the old way of thinking of things, he says there is no “third way.” Which I take as an indicator that my perhaps pseudonymous paper got under his skin. He does say a “shift” in thinking is needed. Amen to that. A shift to a third way.
My book should be out June-ish.