Cox & Mayo

October 31, 2012
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(This article was originally published at Gianluca Baio's blog, and syndicated at StatsBlogs.)

One of my favourite Friends episodes is when Joey finally has a breakthrough and gets his first starring role in the show "Mac & Cheese" (in fact the robot was called C.H.E.E.S.E. $-$ "Computerised Humanoid Electronically Enhanced Secret Enforcer"). 

To me, and I know this is veeeeery mature of me, this has the same comic effect of when I first read a paper by David Cox and Deborah Mayo. These two are of course serious people, doing amazing work in their respective fields (of course, statistics for Sir David; and philosophy of science for Deborah Mayo). But, then again, as Sheldon Cooper, PhD would put it: "what's life without whimsy?"

Anyway, I've had a bit of Cox & Mayo this week; first, I've seen this post on Christian Robert's blog, in which he discusses some of Mayo's position on Bayesian statistics. Mayo works in the field of philosophy of science and is a proposer of the frequentist approach. In fact, as Christian also mentions, her position is quite critical of the Bayesian approach and I too have noticed (although I have to say I have not read as much of her work) that she has a sort of "military resistance" attitude to it.

Perhaps in philosophy of science there is a presumption that only the Bayesian approach has philosophically sound foundations; I can see that we Bayesians may sometimes see ourselves as the "righteous ones" (mainly because we are $-$ only kidding, of course), although I think this probably was a real issue quite a while back; certainly not any more, at least from where I stand. 

If this is indeed the case, maybe her position is justifiable and she serves the purpose of keeping a balanced perspective in the field. In my very limited experience and interaction with that environment, I've been lucky enough to talk quite a few times with people like Hasok Chang (who at some point was my joint boss) and Donald Gillies. The impression I had was that there was no perception that from the philosophical point of view, "most of Statistics is under threat of being overcome (or “inundated”) by the Bayesian perspective" (as Christian put it). I really liked Christian's post and essentially agreed on all accounts.

The second part of this story is about this morning's lecture by David Cox (which was organised by Bianca and Rhian). He talked about the principles of statistics, in what he said was a condensed version of a 5-hours lecture. Of course, it was interesting. He's a very good speaker and it's amazing to see how energetic he still is (he's 88 $-$ I was about to complain that my back is hurting today, but that put me in perspective!).

There were a few points I quite liked and a few more I quite didn't. First, I liked that he slipped in an example in which he implicitly said he's an Aston Villa fan; now I feel justified about putting a bit about Sampdoria in chapter 2 of the book $-$ I can always said I did it like Cox, which to a statistician is quite something...

Also, I liked the distinction he made between what he called "phenomenological" and "substantive" models. The first term indicates all those models that are general enough to be widely applicable (including, as he put it "those strange models that people use to analyse survival data"), but not directly related to the science underlying the problem at hand. Something like: you can "always" use regression analysis, and effectively the same formulation can apply to medicine, agriculture or social science. The maths behind the model is the same. The second term indicates models that are specifically built to describe a specific bit of science; they are thus very much specific, although of course you may not be able to apply them in many cases. A bit like decision models (as opposed to individual data models) in health economics.

What I didn't quite like (but that was to be expected) was his take on Bayesian statistics, and specifically on the subjective/personalistic approach. I think I've heard him talk about it on another occasion, and that time it was even worse (from my Bayesian perspective), but the point is that he basically said that there's no room for such an approach in science, with which I respectfully (but totally) disagree. In fact, as Tom pointed out while we were walking back, at some point he was even a bit contradictory when he framed the significance of RCTs data in terms of the problem a doctor faces when deciding what's the best course of action for the next patient $-$ pretty much a personalistic decision problem!



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