Bayesian Methods and Inference

本研究集中于贝叶斯方法在小面积估计中的理论研究和应用，以及有限总体抽样下贝叶斯鲁棒性和贝叶斯信息的研究。近年来，小面积估计在调查抽样中的应用越来越多。联邦政府各机构参与了对州和地方政府地区的失业率、人均收入、农作物产量等的估计。在典型情况下，单个地区只有少数样本可用，并且可以通过结合来自类似邻近地区的信息来改进对某个区域平均值的估计或对几个区域平均值的同时估计。经验贝叶斯方法和层次贝叶斯方法特别适合于满足这种从相关小领域“借力”的需要。多年来，首席研究员开发了通用的单变量贝叶斯方法，并将其应用于小面积估计。本文的研究是将这些方法推广到多变量小面积估计问题，并对重复调查数据进行分析，即时间序列分析。将具体应用于研究1990年人口普查中计算不足的调整，根据卫生和人类服务部的需要估计三口、四口和五口之家的收入中位数；以及根据劳工统计局的需要对非农业工业机构的所有雇员总数进行估计。主要的理论研究将包括贝叶斯过程的鲁棒性研究，也就是说，贝叶斯过程对偏离假设先验的鲁棒性有多强。这些鲁棒性思想的具体应用将在有限总体抽样的背景下进行。最后的理论研究将包括通过纯后验分析对不同先验的信息含量进行分析研究。高希专业人员有充分的条件来进行拟议的研究。他过去在这一领域的工作产生了重大影响，目前的四个项目应产生重要的方法和应用结果。

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.