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Identification, ranking and selecting hazardous traffic accident locations from a group under consideration is a fundamental goal for traffic safety researchers. Few methods exist that can quantitatively, accurately and easily discriminate between sites that commonly have small and variable observation count periods. One method that embodies all these advantages is the hierarchical Bayesian model, the method proposed in this paper. The particular hierarchical Bayesian approach that we use incorporates expert knowledge about accident sites as a group believed a priori to be exchangeable, the Poisson assumption and a conjugate gamma prior. We then propose three natural strategies for ranking and selecting the most hazardous subgroup of accident locations. Also presented is an especially useful procedure that gives the probability that each particular site is worst and by how much it is worst. All proposed strategies are illustrated using previously published fatality accident data from 35 sites in Auckland, New Zealand.

The purpose of this paper is to illustrate the value of a Bayesian approach in practical problems involving two groups (treatments) which are to be compared. Using practical criteria for comparisons, the advantage of the Bayesian approach will be demonstrated in two situations. Problem I will deal with cholesterol data from two groups of people and it is the aim of the experiment to say which group has the higher cholesterol levels. Problem II will compare two treatments in a clinical trial situation at an interim before the trial is completed. This situation is referred to as interim analysis because only part of the data in the planned trial has been collected. At this interim stage it is desirable to decide whether to stop the experiment now or to continue until the end.

This article considers the variation of the Secretary Problem where at any stage each of the last m applicants are available for employment. We show that the form of the stopping rule which maximizes the probability of employing the best applicant is: stop at the first stage, from r* onwards, when the relatively best applicant is about to become unavailable. A simple algorithm for evaluating r* and the probability of employing the best applicant is outlined.

A Bayesian approach is given for various kinds of empirical Bayes problems. In particular it is shown that empirical Bayes procedures are really non-Bayesian, asymptotically optimal, classical procedures for mixtures. In some situations these procedures are Bayes with respect to some prior and in other situations, there is no prior for which they are Bayes. Several examples of these concepts are given as well as a general theory showing the difference between an empirical Bayes model and a Bayes empirical Bayes model.