论文标题
尖锐的假设和有机基准推断
Sharp hypotheses and organic fiducial inference
论文作者
论文摘要
基本的推论问题类别的特征是存在很大程度的data（或先前）的信念，即模型参数$θ_j$的价值相等或接近指定值$θ^{**} _ j $，例如，这可能会表明缺乏治疗效应或缺乏两种量化的值的价值。本文提出了一种通常适用的“按钮”解决方案，以解决这种类型的问题，该问题避免了尝试将标准的推论（包括贝叶斯方法）应用于此类问题时出现的严重困难。通常，用户实现此解决方案所需的主要音符的唯一输入是分配了data或先前的概率，即参数$θ_j$在狭窄的间隔$ [θ_{j0}，θ_{j1}] $中，该假设假定该$ umport $ the Import的价值$ the $ thy $ tim $ ch^^$ j $ j $。另一方面，通过应用此方法实现的最终结果是在所有参数上方便地是$θ_1，θ_2，\ ldots，θ_k$ the Cholde of Charte的联合data分布。提出的方法是通过将简单的贝叶斯论证与一种称为有机基准推断的方法自然相结合的方法来构建的，该方法是在许多早期论文中开发的。首先，详细介绍和讨论了这种贝叶斯和基准方法的主要理论论点。然后在本文的后半部分中概述了该方法的各种应用和有用的扩展。在适当的情况下，被认为的示例与临床试验数据的分析有关。
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 $θ_j$ was equal or lay close to a specified value $θ^{*}_j$, 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 $θ_j$ lies in a narrow interval $[θ_{j0},θ_{j1}]$ that is assumed to contain the value of interest $θ^{*}_j$. 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 $θ_1,θ_2,\ldots,θ_k$ 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.
