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

摘要提案：0406169 PI：Glen Meeden 客观贝叶斯和设计基方法的综合 有限总体抽样 在有限总体抽样的频率论或设计方法中，先验信息被纳入抽样设计中.然而，在某些情况下，当计算估计的设计权重需要重新调整，然后它可以很难找到合理的方差估计.在贝叶斯方法先验信息通过先验分布.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后验是一种有限总体抽样的客观贝叶斯方法，适用于很少或没有先验信息的情况。研究人员正在开发一个综合的这种客观贝叶斯方法和设计为基础的方法。它有两条主线。在第一个波利亚后被扩展到问题，它不能直接应用，因为额外的先验信息包含在canderaryvariables。这会导致Polya后部的受限或限制性翻转。在第二个贝叶斯模型开发直接包括设计在规范的先验.这样的模型是一个广义的波利亚后验和使用它们可以客观地纳入到一个事先的同类信息是封装在一个design.The调查员正在开发的基本理论和方法来模拟从这些客观的后验，使估计可以在实践中发现和他们的频率属性研究。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，随机样本中的值的平均值被用作总体平均值的估计.然而，除了估计之外，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。这一信息应用于决定样本中应包括哪些单位、估计值和不确定性的适当衡量。调查员正在综合处理这些问题的两种标准办法。 与现有的方法相比，其结果应更有效地利用现有的先验信息，由于政府和其他方面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。

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.