Sharp hypotheses and organic fiducial inference
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尖锐假设与有机置信推断
- 研究问题
- 当事前相信某参数等于或接近特定值时，如何表达这一信念，并形成覆盖模型全部参数的联合数据后分布？
- 方法与思路
- 作者将简单贝叶斯论证与有机置信推断结合，要求用户为包含目标值的窄区间指定事前概率，再构建联合数据后分布。
- 材料陈述的贡献
- 摘要提出面向此类假设的通用推断方案，讨论理论论证、应用和扩展，并在适当情况下联系临床试验数据分析。
- 阅读关注点
- 应核对窄区间与事前概率如何影响结果、联合分布构造是否唯一，以及其校准性质与贝叶斯方法比较的具体依据。
- 阅读边界
- 这是 arXiv 预印本，同行评审与接收未核实。摘要未说明完整适用条件，不能据此确认其通用性或对标准方法的优势。
原文摘要
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.