Bayesian Methods and Inference

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This research concentrates on several theoretical investigations and applications of Bayesian methods to small area estimation, as well as the study of Bayesian robustness in finite population sampling , and Bayesian information. Recently the use of small area estimation has been increasing in survey sampling. Agencies of the Federal Government have been involved in obtaining estimates of unemployment rates, per capita income, crop yields, and so forth, for state and local government areas. In typical instances, only a few samples are available from an individual area, and an estimate of a certain area mean, or simultaneous estimates of several area means, can be improved by incorporating information from similar neighboring areas. Empirical and hierarchical Bayes methods are particularly well-suited to meet this need of "borrowing strength" from related small areas. The principal investigator, over the years, has developed general univariate Bayesian methods with applications to small area estimation. The present research is concerned with the extension of such methods to multivariate small area estimation problems and with the analysis of repeated survey data, which amounts to time series analysis. Specific applications will be made to the study of undercount adjustment in the 1990 census, estimation of median incomes of three-, four-, and five-person families as needed by the Department of Health and Human Services, and the estimation of all employee totals in non-agricultural industrial establishments as needed by the Bureau of Labor Statistics. The principal theoretical investigation will consist of the robustness study of Bayesian procedures, that is, how robust a Bayesian procedure is against departures from the assumed prior. Specific applications of these robustness ideas will be made in the context of finite population sampling. The final theoretical investigation will consist of an analytical study of the information content in different priors through a pure posterior analysis. Profession Ghosh is well equipped to perform the proposed research. His past work in this area has had substantial impacts and the present quartet of projects should yield both important methodological and applied results.