An Attempt to Developing the Hybrid Bayesian Conjugate Analysis

目前研究的目的是允许贝叶斯方法是可接受的通常的统计用户，如频率学家。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。这一点现在很重要，因为这样的模型正变得流行，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给数值计算带来了严重的问题，但由于数值仪器和技术的进步，这一负担已被消除。我们的方法是只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可以接受的先验分布。当部分相对较小时，我们可以期待贝叶斯方法和频率方法的优势，因为我们假设了一个先验分布…更多关于高维参数，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待解决的有趣问题。一个例子是根据特殊函数减少必要的计算。注意，使用特殊函数可以允许我们对分析中出现的函数进行分析求值。研究中的实际模型都是包含一个共同斜率参数的多地层广义线性模型，其误差分布为指数族。该模型的主要兴趣通常放在共同的坡度参数上，其余的分层参数为。回想一下，这样的参数常常被视为讨厌的东西。然而，这种处理是不现实的，但由于可避免的技术原因而被采用。目前的研究表明，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通过地层推断共同参数的实用方法。实际误差分布包括gamma和二项分布，这是我们在实际数据分析中所熟悉的。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，尽管任何结果尚未发表。它涉及检验统计量与预测密度之间的关系。这种密切的关系似乎被理论研究者广泛接受，但没有提出任何明确的检验统计量。请注意，需要进一步的详细研究来实现检验统计量和置信区间。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