摘要翻译：
假设X和Y是暴露和结果的二元变量，我们完全知道Y的分布，给出X的应用。由此我们知道X对Y的平均因果影响。我们现在感兴趣的是，对于一个暴露并显示出积极结果的病例，评估是否是暴露导致了结果。有关的“因果概率”PC通常不是由给定X的Y的分布来确定的，但是可以在其上设置界限，如果我们有关于因果过程的进一步信息，这些界限可以得到改进。在这里，我们考虑了在X和Y之间的完全中介序列的概率结构已知的情况，我们导出了在PC上计算中介上任何数据模式（包括没有数据的情况）的界的一般公式。我们表明，任何完整中介过程的最大和最小上下界都可以在最多包含两个步骤的过程中获得。我们还考虑了具有许多中介体的齐次过程。PC有时可以用负数据识别为0，但即使在无限组介质上用正数据也不能识别为1。这些结果对从一般过程和案例数据的知识中学习因果关系有影响。
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英文标题：
《Bounding Causes of Effects with Mediators》
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作者：
Philip Dawid, Macartan Humphreys and Monica Musio
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. From this we know the average causal effect of X on Y. We are now interested in assessing, for a case that was exposed and exhibited a positive outcome, whether it was the exposure that caused the outcome. The relevant "probability of causation", PC, typically is not identified by the distribution of Y given X, but bounds can be placed on it, and these bounds can be improved if we have further information about the causal process. Here we consider cases where we know the probabilistic structure for a sequence of complete mediators between X and Y. We derive a general formula for calculating bounds on PC for any pattern of data on the mediators (including the case with no data). We show that the largest and smallest upper and lower bounds that can result from any complete mediation process can be obtained in processes with at most two steps. We also consider homogeneous processes with many mediators. PC can sometimes be identified as 0 with negative data, but it cannot be identified at 1 even with positive data on an infinite set of mediators. The results have implications for learning about causation from knowledge of general processes and of data on cases.
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PDF链接：
https://arxiv.org/pdf/1907.00399