Confidence Methods

Abstract

The requirements of the fiducial inference, as laid out by Fisher, entail that the observable quantity as well as the parameter about which the inference is being made be distributed continuously. A simple, pervasive, and important instance in which this condition is not met, is that of estimating the parameter p of a binomial distribution. From a philosophical point of view, in which our chief concern is with the problem of inductive logic, this may well be the most important problem of all: it is the problem, basically, if analyzing the inference that the proportion of A’s that are B’s is likely to be close to the proportion of observed A’s that are B’s.