Mathematical Sciences: Some Bayesian Problems in Sample Survey

这个建议将考虑贝叶斯方法在有限总体抽样中的一些问题中的应用。在过去的几年里，主要研究者帮助开发了一种非信息贝叶斯方法来解决有限人口抽样中的一些问题。它是基于“波利亚后”，是适当的，当一个人的先验信念的单位大致可交换。该项目的第一个主要目标是将“Polya posterior”的基本技术推广到集群抽样领域。这有望为一类重要的问题提供一个灵活而统一的理论。马尔可夫链蒙特卡罗技术的最新发展意味着贝叶斯模型，直到最近一直是计算上棘手的，现在可以研究。这个项目的第二个主要目标是使用这些方法来开发贝叶斯模型的调查抽样时，一个人的先验信念的单位不再是可交换的。在一类模型中，假设单位是部分可交换的，而在另一类模型中，假设种群是由广义的urn过程产生的。这应该产生一个模型的集合，扩展了可用于抽样调查分析的先验信息类型。调查抽样或有限总体抽样中的标准设置假设某些总体中的每个成员都拥有未知数量的感兴趣特征。统计学家感兴趣的是估计与该感兴趣特征相关的量。例如，感兴趣的特征可以是家庭收入、给定城市中所有家庭的人口以及感兴趣的数量，即该城市的平均或中位数家庭收入。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该数量。该项目的主要目标是研究如何使用有关总体的先验信息来构建有关感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各种模型，以获得迄今为止不可能研究的先验信息。

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.