Why during the 1950-1960’s did Jerry Cornfield become a Bayesian?

Joel Greenhouse writes:

I saw your recent paper on Feller [see here and, for a more fanciful theory, here]. Looks like it was fun to write. I recently wrote a paper that asks an orthogonal question to yours. Why during the 1950-1960’s did Jerry Cornfield become a Bayesian? It appeared in Statistics in Medicine – “On becoming a Bayesian: Early correspondences between J. Cornfield and L. J. Savage.”

In his paper, Greenhouse writes:

Jerome Cornfield was arguably the leading proponent for the use of Bayesian methods in biostatistics during the 1960s. Prior to 1963, however, Cornfield had no publications in the area of Bayesian statistics. At a time when frequentist methods were the dominant influence on statistical practice, Cornfield went against the mainstream and embraced Bayes. . . . Cornfield’s interest in Bayesian methods began prior to 1961 and that the clarity of his Bayesian outlook began to take shape following Birnbaum’s ASA paper on the likelihood prin- ciple and his subsequent discussions with Savage.

This is interesting to me because I find Savage to be the least convincing of early modern Bayesian writers. I find Lindley, Good, and Box all to be much more persuasive.

Anyway, here’s what I wrote in reply to Greenhouse: Thanks for sending–this is fascinating. I always thought Cornfield worked in agricultural experiments, but I guess that was because of his name.

The sad thing is: this is no joke!

Anyway, Joel generously replied:

If it makes you feel better during WWII he worked for the Bureau of Labor Statistics and solved a famous a linear programming problem. called the Diet problem which had to do with food, which is pretty close to agriculture.

I’m always glad to hear of others who are interested in the history of statistics.

2 thoughts on “Why during the 1950-1960’s did Jerry Cornfield become a Bayesian?

  1. I found the following abstract on PubMed, which gives a bit more detail on the last quote. Very interesting fellow!

    The contributions of Jerome Cornfield to the theory of statistics, by Zelen M.

    Abstract

    This paper is a review of the contributions of Jerome Cornfield to the theory of statistics. It discusses several highlights of his theoretical work as well as describing his philosophy relating theory to application. The three areas discussed are: linear programming, urn sampling and its generalizations to the analysis of variance, and Bayesian inference. It is not widely known that Jerome Cornfield was perhaps the first to formulate and approximately solve the linear programming problem in 1941. His formulation was made for the famous “Diet Problem”. An early publication introduced the method of indicator random variables in the context of urn sampling. This simple method allowed straightforward calculations of the low order moments for estimates arising from sampling finite populations and was later generalized to the two-way analysis of variance. The application of the urn sampling model to the analysis of variance served to illuminate how one chooses proper error terms for making tests in the analysis of variance table. Jerome Cornfield’s philosophy on applications of statistics was dominated by a Bayesian outlook. His theoretical contributions in the past two decades were mainly concerned with the development of Bayesian ideas and methods. A brief survey is made of his main contributions to this area. A particularly noteworthy result was his demonstration that for the two-sample slippage problem of location, the likelihood function under a permutation setting is uninformative for the slippage parameter. However, the posterior distribution differs from the prior distribution despite the fact that the likelihood is uninformative.

  2. He’s credited as the first person to justify the use odds ratios in case-control studies (that was in 1951 if I’m not mistaken).

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