Controversies in the Foundation of Statistics (Reprint)

This lively and wide-ranging article explores the philosophical battles among Bayesians, classical statisticians (frequentists), and a third group, termed the Fisherians. At this writing, no clear winner has emerged, although the frequentists may currently have the upper hand. The article gives examples of the approach to estimation of the mean of a distribution by each camp, and some problems with each approach. One section discusses Stein's estimator more rigorously than the Scientific American article by Ephron and Morris. Ephron speculates on the future of statistical theory. This article will give you insight regarding the fundamental problems of statistics that affect your work (in particular, as regards credibility). The bases of some common actuarial methods are still controversial. This article is presented as part of a program of reprinting important papers on the foundations of casualty actuarial science. It is reprinted with the generous permission of the Mathematical Association Of America. It originally appeared in the American Mathematical Monthly, Volume 85, Number 4, April 1979, pages 231 to 246.