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.

翻译：一类基础性推断问题具有以下特征：在数据获取前（或先验）对模型参数$\theta_j$的值等于或接近某特定值$\theta^{*}_j$存在显著程度的信念，该特定值可能表示无治疗效果或两变量间缺乏相关性。本文针对此类问题提出一种普遍适用的"按键式"解决方案，该方案规避了在尝试应用标准推断方法（包括贝叶斯方法）时所面临的严重困难。实施该方案时，用户需要提供的主要输入通常是为参数$\theta_j$位于包含目标值$\theta^{*}_j$的窄区间$[\theta_{j0},\theta_{j1}]$这一假设赋予一个数据获取前概率或先验概率。另一方面，应用该方法所获得的最终结果便利地给出了该模型所有参数$\theta_1,\theta_2,\ldots,\theta_k$的联合后数据分布。所提出的方法通过将简单的贝叶斯论证与以往多篇论文中发展的有机信仰推断方法自然结合而构建。首先，详细阐述并讨论了支撑这种贝叶斯-信仰联合方法的主要理论依据。随后，本文后半部分概述了该方法的多种应用及有用扩展。所考虑的示例与临床试验数据分析密切相关。