This proposal considers two essentially unrelated problems in Bayesian statistics. In the first, a problem of long standing, finding tractable non-Gaussian analogs of the Kalman model and filtering algorithm, is studied. Here a promising probability structure is introduced that seems to produce sensible recursive filtering algorithms for discrete data. The proposed work involves the development and implementation of this model. In the second, the problem of finding improved interval estimates of a finite population mean or median is considered. It is well-known that under simple random sampling without replacement with a moderate sample from a skewed population, the usual interval estimates perform poorly. The same can be true in stratified random sampling when the sample sizes within the strata are small. Here a noninformative Bayesian approach, which is based on a generalization of the 'Polya posterior', is suggested as a method for generating improved interval estimates. The principal investigator is an expert in the theory of finite sampling. His continued use of the Bayesian approach to problems in this area and in the development of filtering algorithms for discrete data is well worth pursuing. The theoretical concepts have great potential for extension to other estimation problems in finite sampling and the results should receive considerable attention.
