The likelihood principle / James O. Berger, Robert L. Wolpert

The title of this monograph might give the impression that it is esoteric and mathematical. On the contrary, the monograph discusses the most important differences between the Bayesian and frequentist schools of thought in a manner which is interesting and easy to read.
The authors' belief that "advancement of a subject usually proceeds by applying to complicated situations truths discovered in simple settings'' has led them to present 37 examples which illustrate simple points relevant to the foundations of statistical inference. One way to read the book would be to concentrate on understanding these examples. Note that an index of these examples is provided (on page 200).
Discussions by B. M. Hill, D. A. Lane and L. Le Cam and replies by the authors are included in the monograph. Section 3.4 gives an extension of the likelihood principle to nondiscrete cases. These parts of the text are less readable than the remainder.
Readers who do not accept a Bayesian view of statistics will mostly find that they disagree with the authors on some points. The point at which, like Le Cam, the reviewer fails to accept the authors' reasoning is in Section 3.6.2 where it is assumed that evidence is a well-defined concept. For a single-person decision-making situation the reviewer may be able to accept this. But given two Bayesians who have different subjective opinions despite extensive discussions, there seems to be no completely satisfactory way of pooling those opinions and therefore no definition of evidence which is satisfactory to both of them.
The text is typed with equally-spaced characters, not typeset. However, the typing is easy to read and virtually free from errors. The reviewer recommends that people interested in the foundations of statistics read this monograph, concentrating on understanding the examples which are presented. (MathSciNet)