ABSTRACT
This chapter presents summaries of some of the applications of empirical Bayes (EB) methods that have been published. In most branches of statistics there are data sets that are used repeatedly to demonstrate new techniques or modifications of new ones. The reason is that those data sets are considered to be particularly suitable in the sense of being generated by processes closely approximating the models on which the techniques are based. The same is true of EB methods. The basic data used in the EB analysis comprises two least squares regression coefficients together with an estimated covariance matrix for each law school. Stratified sampling of populations is performed for various reasons, including convenience, the desire to improve precision, and also because results for individual strata may be of interest. Event empirical Bayes ideas are also useful for smoothing out irregularities in individual estimates, especially if they are based on relatively sparse data.
