A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter $\theta_j$ was equal or lay close to a specified value $\theta^{*}_j$, which may, for example, be the value that indicates the absence of a treatment effect or the lack of correlation between two variables. This paper puts forward a generally applicable 'push-button' solution to problems of this type that circumvents the severe difficulties that arise when attempting to apply standard methods of inference, including the Bayesian method, to such problems. Usually the only input of major note that is required from the user in implementing this solution is the assignment of a pre-data or prior probability to the hypothesis that the parameter $\theta_j$ lies in a narrow interval $[\theta_{j0},\theta_{j1}]$ that is assumed to contain the value of interest $\theta^{*}_j$. On the other hand, the end result that is achieved by applying this method is, conveniently, a joint post-data distribution over all the parameters $\theta_1,\theta_2,\ldots,\theta_k$ of the model concerned. The proposed method is constructed by naturally combining a simple Bayesian argument with an approach to inference called organic fiducial inference that was developed in a number of earlier papers. To begin with, the main theoretical arguments underlying this combined Bayesian and fiducial method are presented and discussed in detail. Various applications and useful extensions of this methodology are then outlined in the latter part of the paper. The examples that are considered are made relevant to the analysis of clinical trial data where appropriate.

中文翻译：

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尖锐的假设和有机的基准推论

一类基本的推理问题的特征是，存在相当程度的预数据（或先验）信念，即模型参数 $\theta_j$ 的值等于或接近指定值 $\theta^{ *}_j$，例如，它可能是表示没有治疗效果或两个变量之间缺乏相关性的值。本文针对此类问题提出了一种普遍适用的“按钮式”解决方案，以规避在尝试将包括贝叶斯方法在内的标准推理方法应用于此类问题时出现的严重困难。通常，用户在实现此解决方案时唯一需要的主要注释输入是为参数 $\theta_j$ 位于窄区间 $[\theta_{j0} 的假设分配前数据或先验概率,\theta_{j1}]$ 假定包含感兴趣的值 $\theta^{*}_j$。另一方面，通过应用这种方法获得的最终结果是方便地在相关模型的所有参数 $\theta_1,\theta_2,\ldots,\theta_k$ 上进行联合后数据分布。所提出的方法是通过自然地将简单的贝叶斯论证与称为有机基准推理的推理方法相结合而构建的，该推理方法在许多早期论文中开发。首先，详细介绍并讨论了这种贝叶斯和基准方法相结合的主要理论论据。然后在本文的后半部分概述了该方法的各种应用和有用的扩展。在适当的情况下，考虑的示例与临床试验数据的分析相关。