A David Cox Story

I was writing to somebody at Nuffield College, Oxford about co-authoring a paper, and since we didn’t know each other personally, I told him could ask some people there about me. Looking up to see who was still there (I was a visiting scholar in 2007-2008, I think), I saw with dismay, that Sir David Cox’s name wasn’t listed with the fellows. He’s old, so I thought he must have died, but checking Wikipedia, I see he’s 96 now, but still alive, and my correspondent said he was still coming in to dine in college till covid came along, and published at least one paper last year.

David Cox

That made me think of how kind and genteel David Cox was with me, an economist, when I was visiting, very much in the good old Oxford manner of treating brash but well-meaning Americans. (See To Teach The Senators Wisdom, or, an Oxford Guide-Book, J. C. Masterman, 1952, one of the best guides to Oxford.) Cox, you must understand, is Box-Cox Cox, Cox Regression Cox, someone I had heard of as an undergraduate in the 70’s, the kind of guy who would have a Nobel Prize if they gave them in statistics. Very smart, as we economists say– and a nice guy too.

I thought I’d write up how he was kind to me, since it’s the kind of thing that makes great material for an obituary, but since he’s still alive, I’ll send this to him and it will be encouraging, and if someone’s hard up for David Cox stories for the eventual obituary, they’re free to use it. Not too much to say, actually. Just that I had a statistics idea that year I was visiting Oxford. It went something like this, though I might have my own idea wrong. Suppose you had data from several cities in Indiana and you wanted to estimate the average temperature in Indiana in August. Bloomington has a very accurate thermometer, Gary medium accuracy, and Evansville a really bad thermometer, though all the thermometers are unbiased, as likely to measure too hot as too cold. What’s the best way to estimate the average? The question is whether you should just add up all the observations and take the simple average, or weight the Bloomington data more heavily. The surprising conventional answer is that you should (can?) just take the simple average. I thought I’d proved that you should weight Bloomington more heavily. Moreover, I’d coded a numerical simulation that confirmed my proor and intuition. If I was right, this would be a big deal, because this is so common a problem that lots of people would like to be able to improve the efficiency of their estimates (both methods get the same, correct, answer on average; the issue is whether you can improve efficiency by using the extra information and reduce the variance of your estimate).

Nuffield dining hall

What I say is the conventional wisdom on that problem seems so counterintuitive that I feel like maybe my memory is flawed, but maybe that’s why I was so keen on my idea. Anyway, I remember how kind Cox was in listening to me describe it. In Nuffield, the lunchtime custom was that everyone, fellows, students, visitors, etc., would sit at the next opening on the long table, everyone being equal in status and economists, statisticians, sociologists, and political scientists mixing together (we kshatriyas suffered sitting with the sudras and untouchables, but it was good for us). I was sitting next to him, and when we went down to the common room for coffee after lunch, as was the custom, he asked me to join him. I described my idea. He asked if I’d done a numerical simulation, and I told him I had. Indeed, if I hadn’t, I would have been too scared to broach the idea to him, since I was experienced enough to know that “mathematical proof” is at the mercy of a sign error in the calculations. He listened intently. He didn’t dismiss the idea, and thought it was worth thinking about. Alas, I later discovered I had indeed made a math error in my proof. Moreover, I’d made a coding error in my simulation too, and the thing about simulations to confirm that a new method makes a difference the results is that pretty much any coding error will make a difference in the results too, half positive and half negative. So I had to go back some time later and tell him my grand idea was fatally flawed and would never see light of day again. And he was kind then, too.

So that’s my memory of David Cox.