An Attempt to Developing the Hybrid Bayesian Conjugate Analysis

本研究的目的是使贝叶斯方法为常见的统计用户(如频率学家)所接受。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，因为这样的模型变得流行起来，以便应用现实的模型来充分解释研究中的数据集的特征。虽然具有高维参数的模型会引起与数值计算有关的严重问题，但由于数值仪器和技术的进步，这种负担被消除了。我们的方法是假设只对部分参数进行先验分布。这是因为参数的一部分是有争议的，而且不容易假定利益相关者双方都能接受的先验分布。当比例相对较小时，我们可以预期贝叶斯方法和频率方法的优点，因为我们假设先验分布…更多的是关于高维参数，但不要假设有争议的参数的先验分布。这种方法引发了各种需要解决的有趣问题。一个例子是根据特殊函数减少必要的计算。请注意，使用特殊函数可以使我们能够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层广义线性模型，该模型包含一个通用的穿过地层的斜率参数，其中误差分布为指数族。这个模型的主要兴趣通常放在共同的斜坡参数上，其余的地层参数是次要的。回想一下，这种参数通常被视为滋扰。然而，这种治疗是不现实的，但之所以采用这种治疗方法，是因为可以避免的技术原因。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通过地层推断共同参数的方法。实际误差分布包括伽马分布和二项分布，这在实际数据分析中是很常见的。作为我们的研究计划的副产品，我们得到了一个意想不到的结果，尽管到目前为止还没有发表任何结果。它涉及到检验统计量与预测密度之间的关系。这一密切关系在理论研究者中已被广泛接受，但并未提出任何显式检验统计量。请注意，需要进行进一步的详细研究，以实施测试统计数据和可信区间。较少

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