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Bayesian, classical and hybrid methods of inference when one parameter value is special

机译：一个参数值特殊时的贝叶斯，经典和混合推理方法

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This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree of prior belief that the true value of the parameter lies in this interval. A clear justification of the practical importance of this problem is provided. The main difficulty with the standard Bayesian solution to this problem is discussed and, as a result, a pseudo-Bayesian solution is put forward based on determining lower limits for the posterior probability of the parameter lying in the special interval by means of a sensitivity analysis. Since it is not assumed that prior beliefs necessarily need to be expressed in terms of prior probabilities, nor that post-data probabilities must be Bayesian posterior probabilities, hybrid methods of inference are also proposed that are based on specific ways of measuring and interpreting the classical concept of significance. The various methods that are outlined are compared and contrasted at both a foundational level, and from a practical viewpoint by applying them to real data from meta-analyses that appeared in a well-known medical article.
机译：本文考虑了在以参数的给定值为中心的窄间隔被认为是特殊的情况下对参数进行统计推断的问题，这被解释为意味着在很大程度上相信该参数的真实值在于在此间隔内。提供了此问题的实际重要性的明确理由。讨论了使用标准贝叶斯解决方案解决此问题的主要困难，结果，通过灵敏度分析确定参数位于特殊区间的后验概率的下限，提出了伪贝叶斯解决方案。由于没有假定必须先验概率就必须表达先验信念，也不应该假设后数据概率必须是贝叶斯后验概率，因此还提出了基于特定量度和解释经典方法的混合推理方法。意义的概念。概述的各种方法都在基础级别上进行了比较和对比，并从实际角度将它们应用于著名医学文章中出现的荟萃分析的真实数据中。

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