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An Attempt to Developing the Hybrid Bayesian Conjugate Analysis

开发混合贝叶斯共轭分析的尝试

基本信息

批准号：
18500220
负责人：
YANAGIMOTO Takemi
金额：
$ 1.75万
依托单位：
Chuo University (2007)The Institute of Statistical Mathematics (2006)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

项目摘要

The aim of the present research is to allow Bayesian methods to be acceptable for usual statistical users such as frequentists. It becomes now apparent that Bayesian methods are useful when the model employed contains a high-dimensional parameter This aspect is now important, since such a model is becoming popular in order to apply a realistic model explaining adequately characteristics of the data set in the study. Although a model having a high-dimensional parameter gave rise to serious problem pertaining to numerical computations, this burden is eliminated due to advances in numerical instruments and techniques.Our approach is to assume a prior distribution only on a part of parameters. This is because a part ofparameters are subject to controversy, and it is not easy to assume a prior distribution acceptable for both sides of stakeholders. When the portion is relatively small, we can expect both advantages of Bayesian and frequentist approaches, since we assume a prior distribution … More on a high-dimensional parameter but do not assume a prior distribution on parameters under controversy. This approach gives rises to various interesting problems to be solved. An example is to reduce necessary computations in terms of the special functions. Note that the use of special functions can allow us the analytical evaluation of the functions appeared in the analysis. Actual models in the study contain the generalized linear model with multiple strata containing a common slope parameter through strata where an error distribution is in the exponential family. A primary interest in this model is usually placed on the common slope parameter, and the remaining stratum-wise parameters are.of secondary interest Recall that such parameter was often treated as nuisance. Such a treatment, however is unrealistic but was employed because of avoidable technical reasons. The present research showed that our research program meets with the need of the current theoretical statistics. We succeeded in proposing several practical methods for inference of a common parameter through strata. The actual error distributions cover the gamma and binomial distributions, which are familiar in the practical data analysisAs a byproduct of our research program we obtained an unexpected result, though any result is not published as yet. It pertains to the relation between the test statistic and the predictive density. It looks that the close relation is widely accepted among theoretical researchers, but any explicit test statistic is no proposed. Note that further detailed studies will be necessary to implement a test statistic and a confidence interval. Less

本研究的目的是让贝叶斯方法是可以接受的通常的统计用户，如frequentist。现在很明显，当所采用的模型包含高维参数时，贝叶斯方法是有用的。这方面现在很重要，因为这样的模型正在变得流行，以便应用一个现实的模型来充分解释研究中数据集的特征。虽然具有高维参数的模型会给数值计算带来严重的问题，但由于数值仪器和技术的进步，这种负担已经消除。我们的方法是仅假设部分参数的先验分布。这是因为部分参数存在争议，并且不容易假设利益相关者双方都能接受的先验分布。当这部分相对较小时，我们可以预期贝叶斯和频率论方法的优点，因为我们假设先验分布 ...更多信息但不假设有争议的参数的先验分布。这种方法产生了各种有趣的问题要解决。一个例子是减少特殊函数方面的必要计算。注意，特殊函数的使用可以允许我们对分析中出现的函数进行分析评估。研究中的实际模型包含多个地层的广义线性模型，其中包含通过地层的共同斜率参数，其中误差分布为指数族。在这个模型中，主要的兴趣通常放在共同的坡度参数上，其余的分层参数是次要的。回想一下，这种参数通常被视为讨厌的参数。然而，这种处理是不现实的，但由于可以避免的技术原因而采用。本研究表明，我们的研究方案符合当前理论统计的需要。我们成功地提出了几种实用的方法来推断一个共同的参数通过地层。实际的误差分布包括伽玛分布和二项分布，这是在实际数据分析中熟悉的。作为我们研究计划的副产品，我们得到了一个意想不到的结果，虽然任何结果尚未公布。它涉及检验统计量与预测密度之间的关系。这种密切关系似乎已被理论研究者广泛接受，但尚未提出任何明确的检验统计量。请注意，需要进一步详细的研究来实现检验统计量和置信区间。少