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For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin´s recent book, Statistical Inference , which presents an approach to statistical hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and illustrates his method using some simple examples of inference from iid data and two-way tests of independence. We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.

It is a rare event in the statisticalworld for a book reviewto take 15 pages (plus references). The three reviewers are all eminent in the profession, and have tried to be scrupulously careful in their reviewof a bookwhosemain principle they firmly dispute as non-Bayesian, and which they find not to be useful in their work. The length of the review demonstrates the seriousnesswith which they regard the book′s approach, and the importance to them of denying its relevance to either Bayesian analysis or practical data analysis with complex data. In responding to the authors′ review, I found it helpful to place our different views in the framework of Thomas Kuhn′s (1962) discussion of paradigm changes in science.

Starting from the requirement that risk of financial portfolios should be measured in terms of their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize convex loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of the risk estimators associated with the family of loss-based risk measures: we provide a general criterion for the qualitative robustness of the risk estimators and compare this criterion with a sensitivity analysis of estimators based on influence functions. We find that the risk estimators associated with convex loss-based risk measures are not robust.

In this paper we give sufficient conditions for solving two-person zero sum stopping games. These are games where the strategy set of the two players are stopping times of a diffusion X . Our method is based on the study of harmonic functions for the diffusion and it is similar to the approach of solving optimal stopping problems developed in [2]–[4], and [12].

This paper deals with the two-sample Kolmogorov–Smirnov test and its biasedness. This test is not unbiased in general in case of unequal sample sizes. We identify most biased distributions for some values of significance level α . Moreover, we discovered that there exists numbers of observations and significance levels α such that this test is unbiased at level α .