Mathematical Sciences: Some Bayesian Problems in Sample Survey

数学科学：抽样调查中的一些贝叶斯问题

• 批准号: 9401191
• 负责人: Glen Meeden
• 金额: $ 6万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401191&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Bayesian; Problems

This proposal will consider the application of the Bayesian methodology to some problems in finite population sampling. Over the past several years the principle investigator has helped to develop a noninformative Bayesian approach to some problems in finite population sampling. It is based on the `Polya posterior' and is appropriate when one's prior beliefs about the units are roughly exchangeable. The first major goal of this project is to extend the techniques underlying the `Polya posterior' to the area of cluster sampling. This promises to yield a flexible and unified theory for an important class of problems. Recent developments in Markov chain Monte Carlo technology mean that Bayesian models which until recently have been computationally intractable can now be studied. The second major goal of this project is to use these methods to develop Bayesian models for survey sampling when one's prior beliefs about the units are no longer exchangeable. In one class of models to be considered the units will be assumed to be partially exchangeable, while in another class the populations will be assumed to be generated by a generalized urn processes. This should yield a collection of models that extends the type of prior information that can be used in an analysis in sample survey. A standard setting in survey sampling or finite population sampling assumes each member of some population possesses an unknown amount of a characteristic of interest. The statistician is interested in estimating a quantity related to this characteristic of interest. For example the characteristic of interest could be household income, the population all households in a given city and the quantity of interest the average or median household income for the city. The statistician will then use the values of the characteristic in a sample drawn from the population to estimate this quantity. The major goal of this project is to study how prior information about the population can be used to construct sensible estimates about the quantity of interest. It will use recent developments in computer simulation to investigate various models for prior information which up until now have been impossible to study.

本提案将考虑贝叶斯方法在有限总体抽样中的一些问题的应用。在过去的几年里，首席研究员帮助开发了一种非信息贝叶斯方法来解决有限总体抽样中的一些问题。它基于“Polya posterior”，当一个人对单位的先验信念大致可交换时，它是合适的。该项目的第一个主要目标是将“聚后验”技术扩展到聚类采样领域。这将为一类重要的问题提供一种灵活而统一的理论。马尔可夫链蒙特卡罗技术的最新发展意味着直到最近还难以计算的贝叶斯模型现在可以研究了。该项目的第二个主要目标是，当一个人对单位的先验信念不再可交换时，使用这些方法开发调查抽样的贝叶斯模型。在一类要考虑的模型中，将假定单元是部分可交换的，而在另一类中，将假定种群是由广义的urn过程产生的。这将产生一组模型，扩展可用于样本调查分析的先验信息类型。调查抽样或有限总体抽样的标准设定假设某个总体的每个成员都具有未知数量的感兴趣的特征。统计学家感兴趣的是估计与该感兴趣的特性相关的数量。例如，利息的特征可以是家庭收入，人口，所有家庭在一个给定的城市和利息的数量，平均或中位数家庭收入的城市。然后统计学家将使用从总体中抽取的样本中的特征值来估计这个数量。该项目的主要目标是研究如何使用有关人口的先验信息来构建有关兴趣数量的合理估计。它将利用计算机模拟的最新发展来研究到目前为止不可能研究的先验信息的各种模型。