Friday, June 6, 2014

Frequentist vs. Bayesian Analysis

"Statisticians should readily use both Bayesian and frequentist ideas."

So begins a 2004 paper by Bayarri and Berger, "The Interplay of Bayesian and Frequentist Analysis", Statistical Science, 19(1), 58-80.

Let's re-phrase that opening sentence: "Econometricians should readily use both Bayesian and frequentist ideas."

Before turning to economics, my undergraduate training was in statistics and pure mathematics. My statistical training (in the 1960's) came from professors who were staunchly Bayesian - at a time when it was definitely "them and us". With few exceptions, the attitude was that "if you're not with us, then you're against us". And this was true on both sides of the Frequentist-Bayesian divide.

Hardly a healthy situation - but we've seen similar philosophical divisions throughout the history of economics, and in pretty much every other discipline at some point.

After a very orthodox training in econometrics (based largely on the texts of Johnston, and Malinvaud) I ended up doing my Ph.D. dissertation on some problems in Bayesian econometrics - supervised by a wonderful man who probably didn't have a Bayesian bone in his body. My first J. Econometrics paper looked at some of the sampling properties of certain Bayes estimators. How non-Bayesian can you get?

So, I've always told students that they need to be flexible in their econometric thinking, and they need to be prepared to use both frequentist and Bayesian tools. Time has proved me right, I believe. Modern econometric practice takes advantage of a healthy mix of ideas and techniques drawn from both tool boxes.

Yes, this has been made possible by the considerable advances that we have seen in computing methods and power in recent decades. But it's also reflected something of a shift in the mind-set of statisticians and econometricians alike.

Here's the concluding section of the Bayarri and Berger paper, in its entirety (pp.77-78):
"It seems quite clear that both Bayesian and frequentist philosophy are here to stay, and that we should not expect either to disappear in the future. This is not to say that all Bayesian or all frequentist methodology is fine and will survive. To the contrary, there are many areas of frequentist methodology that should be replaced by (existing) Bayesian methodology that provides superior answers, and the verdict is still out on those Bayesian methodologies that have been exposed as having potentially serious frequentist problems.
Philosophical unification of the Bayesian and frequentist positions is not likely, nor desirable, since each illuminates a different aspect of statistical inference. We can hope, however, that we will eventually have a general methodological unification, with both Bayesian and frequentists agreeing on a body of standard statistical procedures for general use"
I hope that student followers of this blog will take the time to read the Bayarri and Berger paper, and to learn more about Bayesian methods.

© 2014, David E. Giles