A Synthesis of Objective Bayesian and Designed Based Methods for Finite Population Sampling

客观贝叶斯综合和有限总体抽样设计方法

• 批准号: 0406169
• 负责人: Glen Meeden
• 金额: --
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0406169&HistoricalAwards=false
• 关键词: Synthesis; Objective; Bayesian; Designed; Based

ABSTRACTproposal: 0406169PI: Glen Meeden A synthesis of objective Bayesian and designed based methods for finite population sampling Project Abstract In the frequentist or design approach to finite population sampling priorinformation is incorporated in the sampling design. However in some cases when calculating estimates the design weights need to be readjusted, and then it can be difficult to find sensible estimates of variance.In the Bayesian approach prior information is incorporated througha prior distribution. Since the posterior distribution does not depend on the design it has been difficult to theoretically reconcile the two approaches. The Polya posterior is an objective Bayesian approach to finite population sampling that is appropriate when littleor no prior information is available. The investigator is developing a synthesis of this objective Bayesian approach and the designbased approach. It has two main threads. In the first the Polya posterior is extended to problems where it cannot be applied directly because of additional prior information contained in auxiliaryvariables. This leads to a constrained or restrictedversion of the Polya posterior. In the second Bayesian models aredeveloped which directly include the design in the specification of the prior. Such models are a generalization of the Polya posterior and using them one can objectively incorporate into a prior the same kind of information that is encapsulated in a design.The investigator is developing the underlying theory and methods tosimulate from these objective posteriors so that estimators can be found in practice and their frequentist properties studied. One of the most basic problems of statistics is making an inference about a population based on a sample collected from the population.When little is known about the population the mean of thevalues in a random sample is used as an estimate of the populationmean. However in addition to the estimate one also needs a sensible measure of its uncertainty or variance. In mostsituations there is prior information available about the population. This information should be used in deciding what units are to be included in the sample, the value of the estimate and the appropriate measure of uncertainty. The investigator is working on a synthesis of the two standard approaches to these problems. The results should make more effective use of available prior information than present methods.Because of the many surveys done each year by government and others improving survey practice is of great practical significance.

有限总体抽样的客观贝叶斯方法和基于设计的方法的综合研究项目摘要：在有限总体抽样的频率论或设计方法中，将先验信息纳入抽样设计。然而，在某些情况下，当计算估计时，需要重新调整设计权重，然后很难找到合理的方差估计。在贝叶斯方法中，先验信息通过先验分布被纳入。由于后验分布不依赖于设计，因此很难从理论上调和这两种方法。Polya后验是一种客观的贝叶斯方法，用于有限总体抽样，适用于很少或没有可用的先验信息。研究者正在开发一种综合这种客观贝叶斯方法和基于设计的方法。它有两个主线程。在第一种情况下，Polya后验被扩展到由于辅助变量中包含额外的先验信息而不能直接应用的问题。这导致后息肉受限。在第二个贝叶斯模型的发展，直接包括设计在规范的先验。这些模型是Polya后验的概括，使用它们可以客观地将封装在设计中的相同类型的信息合并到先验中。研究人员正在开发从这些客观后验进行模拟的基本理论和方法，以便在实践中发现估计器并研究其频率特性。统计学最基本的问题之一是根据从总体中收集的样本对总体进行推断。当对总体知之甚少时，使用随机样本中值的平均值作为总体平均值的估计。然而，除了估计之外，人们还需要对其不确定性或方差进行合理的测量。在大多数情况下，有关于人口的先验信息。这些信息应用于决定样本中应包括哪些单位、估计值和不确定度的适当度量。研究人员正在研究解决这些问题的两种标准方法的综合。结果应该比目前的方法更有效地利用可获得的先验信息。由于政府和其他机构每年都要进行大量的调查，因此改进调查实践具有重要的现实意义。