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

建议：0406169PI：Glen Meeden有限总体抽样的目标贝叶斯和设计方法的综合项目摘要在抽样设计中采用了有限总体抽样先验信息的频率或设计方法。然而，在某些情况下，在计算估计时，需要重新调整设计权重，这样就很难找到合理的方差估计。在贝叶斯方法中，先验信息是通过先验分布纳入的。由于后验分布不依赖于设计，因此很难在理论上协调这两种方法。Polya后验是有限总体抽样的一种客观贝叶斯方法，适用于先验信息较少或没有先验信息的情况。研究人员正在开发这一客观贝叶斯方法和基于设计的方法的综合。它有两条主线。首先，将Polya后验方法推广到由于辅助变量中包含额外先验信息而不能直接应用的问题。这导致了限制或限制版本的Polya后部。在第二章中，建立了贝叶斯模型，将设计直接包含在前人的规范中。这类模型是Polya后验的推广，使用它们可以客观地将包含在设计中的相同信息合并到先验中。研究人员正在开发从这些客观后验模拟的基本理论和方法，以便在实践中找到估计器，并研究它们的频率特性。统计学中最基本的问题之一是基于从总体中收集的样本来推断总体。当对总体知之甚少时，随机样本中的值的平均值被用作对总体平均值的估计。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衡量。在大多数情况下，都有关于人口的事先信息。这些信息应用于决定样本中应包括哪些单位、估计值和适当的不确定度度量。研究人员正在研究解决这些问题的两种标准方法的综合。调查结果应该比目前的方法更有效地利用现有的先验信息。由于政府和其他部门每年都会进行许多调查，因此改进调查实践具有重要的现实意义。

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.