Topics in Statistical Inference

Abstract

In the preceding chapters, we have based inferences about an unknown parameter θ on the likelihood function itself (Chapters 9 and 10) or on tests of significance (Chapters 13, 14 and 15). These tests were themselves closely related to the likelihood function through the use of sufficient statistics and the likelihood ratio criterion. In Sections 1 and 2 below, we consider two additional methods for making inferences about an unknown parameter. With both the fiducial argument and Bayesian methods, information concerning θ is summarized in a probability distribution defined on the parameter space. For Bayesian methods one requires prior information about θ which is also in the form of a probability distribution. For the fiducial argument, θ must be completely unknown before the experiment.

This chapter may be omitted on first reading.