Glen Meeden

For the past few years I have been interested in finite population sampling. One of the attractive features of this area is the discrete nature of most of the problems. This allows one to address the basic statistical issues without worrying about mathematical complications. In particular it permits one to compare the frequentist and Bayesian paradigms in an important yet simple setting. Finite population sampling is one area where everyone agrees that the statistician must make use of prior information. As a Bayesian I find it somewhat disappointing that Bayesian methods are not used more in practice. The problem is that for a large population, and real populations are often large, it is quite difficult to specify sensible prior distributions. On the other hand a frequentist using such techniques as stratification has a straightforward method of using certain types of prior information. I have been interested in the problem of incorporating various levels of prior information into the analysis in a Bayesian-like way without actually specifying a prior distribution. Although this sounds contradictory, it is possible. In some cases, when little prior information is available, it leads to a noninformative Bayesian justification of many of the usual frequentist methods. In other cases, when more prior information is present, it leads to sensible procedures for problems where no convenient frequentist method is available.