Statistical Information and Likelihood

Abstract

In Part I our main concern was with the notion of statistical information in the data, and with some general principles of data analysis. Now we turn our attention from principles to a few methods of data analysis. By a non-Bayesian likelihood method we mean any method of data analysis that neither violates ℒ-the likelihood principle — nor explicitly incorporates into its inference making process any prior information (that the experimenter may have about the parameter ω) in the form of a prior probability distribution over the parameter space Ω . The origin of most of such methods may be traced back to the writings of R.A. Fisher. In this section we list several such methods. To fix our ideas, let us suppose that Ω is either discrete or an interval subset of the real line. In the latter case, we shall also suppose that the likelihood function L(ω) is a smooth function and has a single mode (whenever such an assumption is implicit in the method).