Saturday, July 16, 2011

A Bayesian and Non-Bayesian Marriage

There's no doubt that the unholy rift between Bayesian and non-Bayesian statisticians, and econometricians, is a thing of the past. And thank goodness for that, because both parties have so much to offer each other.

It wasn't that long ago that it was a case of "them or us" - you had to take sides. That was pretty much the case when I wrote my Ph.D. dissertation in Bayesian econometrics in the early 1970's. These days, most of us are pretty comfortable about using a blend of principles and techniques that are drawn from both camps. It's all about taking a flexible approach, and recognizing that sometimes you need more than one set of tools in your tool box.

Historically, we had the school I'll loosely call the "frequentists" in the blue corner, and the Bayesians in the red corner. I'm not going to try and list the key players in each group. However, the big name that comes to mind in the blue corner is Sir Ronald A. Fisher, who gave us the concept of the "likelihood function", and maximum likelihood estimation.

In the red corner, George E. P. Box has to be numbered as one of the most influential Bayesian statisticians, though his statistical interests were quite broad. Born in England, he later moved to the U.S.A., served as Director of the Statistical Research Group at Princeton University, and  founded the Department of Statistics at the University of Wisconsin (Madison) in 1960.

Apart from anything else, econometricians will know George Box from Box-Jenkins time-series analysis, and the Box-Cox transformation. In addition, George penned the oldest song, "There's No Theorem Like Bayes' Theorem",  in The Bayesian Songbook. See my earlier post on this here.

So, what's the interesting connection between Fisher and Box? Well, among the many professional awards that Box received was  the A.S.A's R. A. Fisher Lectureship in 1974.

But it gets better. Box married Joan Fisher, the second of Fisher's five daughters.

I like that! 

© 2011, David E. Giles

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