A Simple Problem with Strikingly Different Frequentist and Bayesian Solutions

Abstract

Suppose that equal-sized samples are drawn from two normal populations which have unknown means but known and equal standard deviations. Then the paper considers the problem of making probabilistic statements about whether both population means exceed some lower bound. It seems natural to the author to expect procedures for computing this bound to have the property that the bound increases monotonically with the sample means observed. The paper, however, shows that whilst this is true of Bayesian procedures, it is, surprisingly, in general untrue of frequentist procedures.