This book is the reference on the Liklihood Principle, linking it to the Bayesian paradigm in a sharp and convincing way.

Sometimes a frequentist measure of the performance of a procedure - such as a sampling inspection plan or a diagnostic test - is specified, by contract or law, to be of primary interest. Then, of course, the LP (when stated for θ alone) does not apply. (iii) There can be ambiguities in the definition of the likelihood function. The problem can usually be resolved, however, by the approaches discussed in Sections 3.4 and 3.5. (iv) There can be situations in which the choice of experiment conveys

consequence of the LP. n This is immediate from (4.2.2) in that I n11(θ) is proportional to π fQ(x.)» θ 1 x i =l which does not depend on the stopping rule. For derivation of the SRP in general (from the RLP) see Section 4.2.6. CONSEQUENCES AND CRITICISMS OF THE LP AND RLP 77 4.2.3 Positive Implications A recurring problem in classical statistics is that of optional stopping. Ideally (from a classical viewpoint) an experimenter chooses his stopping rule before experimentation, and then

distribution, is relevant to conclusions about Θ. Section 4.3.2 considers the situation of fixed (nonrandom) censoring, and establishes a version of the irrelevance of censoring mechanisms called Censoring Principle 1. One of the implications of Censoring Principle 1 is that the evidential import of an uncensored observation, from an experiment in which censoring was possible, is the same as the identical observation from an uncensored version of the experiment. CONSEQUENCES AND CRITICISMS OF

however.) Also, much of the theory is still based on frequentist (though partly conditional) measures, and hence violates the LP. Of course, many researchers in the field study the issue solely to point out inadequacies in the frequentist viewpoint, and not to recommend specific conditional frequentist measures. Indeed, it is fairly clear that the existence of relevant subsets, such as in Example 6, is not necessarily a problem, since when viewed completely conditionally (say from a Bayesian

paradox. J. Amer. Statist. Assoc. 77, 325-351. SMITH, A. F. M. and SPIEGELHALTER, D. J. (1980). Bayes factors and choice criteria for linear models. J. Roy. Statist. Soc ZELLNER, A. (1984). B 42, 213-220. Posterior odds ratios for regression hypotheses: considerations and some specific results. University of Chicago Press, Chicago. general In Basic Issues in Econometrics. DISCUSSION: AUXILIARY PARAMETERS AND SIMPLE LIKELIHOOD FUNCTIONS BY PROFESSORS M. J. BAYARRI AND M. H. DEGROOT