When Should One Be a Bayesian?

• Activity Number: 363
• Type: Roundtables
• Date/Time: Tuesday, July 31, 2012 : 12:30 PM to 1:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Francisco J. Samaniego*+
• Companies: University of California at Davis
• Keywords: Bayes ; frequentist ; point estimation ; mean squared error ; Bayes risk ; winners and losers

Abstract

While virtually all formally trained statisticians have studied both frequentist and Bayesian statistical methods, rather few have had courses or formal discussions featuring a comparative analyses of the two approaches. In particular, most have not carefully considered the question "When should one be a Bayesian?" Instead, by tradition, convenience or inclination, many statisticians simply make the choice between frequentist and Bayesian methods on an ad hoc or practical basis, depending on the application at hand. In today's discussion, the host will address this question (in the context of "estimation" problems) and will propose a particular way of thinking about it. Evidence will be presented which supports the proposition that there exists a threshold in the space of prior distributions which separates "good priors" from "bad priors" in any given estimation problem. Clues on answering the question above can be drawn from the general nature of that threshold. (For details, see "A Comparison of the Bayesian and Frequentist Approaches to Estimation" (Springer, 2010) by F. J. Samaniego). At this roundtable lunch, we'll simply aim at having a good conversation on the topic!