Comment on Poirer: The Subjective Perspective of a "Spiritual Bayesian"

P rofessor Dale Poirier has preached a rousing sermon for the Bayesian cause, and in doing so has concisely exposed some of the cracks in the foundations of statistics. One of these cracks is the very interpretation of the concept of probability, a philosophical question that has never been fully resolved and has led to the schism that currently exists in statistics between the Bayesian and classical schools. The paper is valuable for econometricians because it challenges them to think more deeply about the meaning of the statistical procedures they employ. It certainly did that for me. However a basic question was not addressed in the paper; namely, what is the purpose of statistical inference? I think the answer to this question has at least as much bearing upon whether someone adopts Bayesian or classical methodology as whether one interprets the meaning of probability in subjectivist or frequentist terms. Certainly beliefs about the proper "purpose" of statistical inference diverge every bit as much as do beliefs about the meaning of probability. Many people, especially statisticians, think the purpose is "prediction," a view Poirier sees as favoring the Bayesian school. Others, such as Ed Prescott, think the purpose is "measurement." Under this view, the parameters to be inferred or measured are real physical quantities and the only source of randomness is measurement error. Since physical quantities have an existence independent of our mental representations of them, this view leads one to avoid the subjective Bayesian approach in favor of "objective" classical methods. Still others