A Noninformative Bayesian Approach to some Finite Population Problems when Auxiliary Variables are Present

存在辅助变量时一些有限总体问题的非信息贝叶斯方法

• 批准号: 9971331
• 负责人: Glen Meeden
• 金额: $ 7.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971331&HistoricalAwards=false
• 关键词: Noninformative; Bayesian; Approach; some; Finite

9971331In finite population sampling in addition to the characteristic of interest, there are often auxiliary variables present which contain information about the characteristic. For example, a priori the population means or some of the population quantiles for these auxiliary variables could be known. Classical theory has developed a variety of methods to exploit this information with different levels of overall effectiveness. The Polya posterior was developed as a noninformative Bayesian approach to finite population sampling when little or no prior information is available. The goal of the proposed research is to extend the Polya posterior to problems where auxiliary variables are present. This will be done by restricting the Polya posterior in a natural way so that given a sample simulated copies of the entire population can be generated which satisfy the constraints induced by the prior knowledge about the auxiliary variables. Statistical inference can then be carried out using the simulated populations in the usual Bayesian manner. The two main technical problems will be to develop the underlying theory and the techniques for implementing the simulations which are consistent with the prior information at hand. This allows for a coherent approach to problems which standard theory must now consider individually. Several problems will be identified were certain types of prior information which are often presently ignored can be used in an objective and effective way. The resulting noninformative Bayesian procedures should have good frequentist properties.A fundamental problem of statistics is making inferences about a population when information is available only about a sample or subset of the individuals making up the population. For example, we may want to estimate how many days a typical worker is absent because of illness during a year in a given industry. In addition to the information in the sample, we may also know the average age or median education level for all the workers in the industry. Statisticians have developed various methods to handle such problems depending on what kind of information beyond the sample is at hand. Some methods work much better than others. In this research we will study a general approach which can effectively make use of a variety of types of information. This is done by using the data in the sample and the prior information to construct simulated or random copies of the entire population which are consistent with both the sample data and the prior information. By considering the variability among these randomly generated copies of the population one can find not only an estimate of the quantity of interest but a measure of uncertainty associated with the estimate.

在有限总体抽样中，除了感兴趣的特征外，通常还存在包含有关该特征的信息的辅助变量。例如，这些辅助变量的总体平均值或某些总体分位数的先验可以是已知的。经典理论已经发展出各种方法来开发这些信息，并具有不同程度的整体有效性。Polya后验是在先验信息很少或没有先验信息的情况下发展起来的有限总体抽样的无信息贝叶斯方法。建议研究的目标是将Polya后验扩展到存在辅助变量的问题。这将通过以自然的方式限制Polya后验来实现，以便在给定样本的情况下，可以生成满足关于辅助变量的先验知识所引起的约束的整个总体的模拟副本。然后，可以使用模拟的总体以通常的贝叶斯方式进行统计推断。两个主要的技术问题将是开发与手头上的先验信息一致的基本理论和实施模拟的技术。这为标准理论现在必须单独考虑的问题提供了一种连贯的方法。如果目前经常被忽视的某些类型的先验信息能够以客观和有效的方式加以利用，将会发现若干问题。由此产生的非信息性贝叶斯过程应该具有良好的频率特性。统计学的一个基本问题是，当信息仅关于组成总体的个体的样本或子集时，对总体进行推断。例如，我们可能想要估计在给定行业中，一个典型的工人在一年中因病缺勤的天数。除了样本中的信息外，我们还可以知道该行业所有工人的平均年龄或中位数教育水平。统计学家已经开发出各种方法来处理这些问题，这取决于手头有什么样本以外的信息。有些方法的效果比其他方法好得多。在这项研究中，我们将研究一种能够有效利用各种类型信息的通用方法。这是通过使用样本中的数据和先验信息来构建与样本数据和先验信息两者一致的整个总体的模拟或随机拷贝来实现的。通过考虑这些随机生成的种群副本的可变性，人们不仅可以找到感兴趣的数量的估计，而且可以找到与估计相关的不确定性的度量。