In this paper, we introduce a new causal framework capable of dealing with probabilistic and non-probabilistic problems. Indeed, we provide a direct causal effect formula called Probabilistic vAriational Causal Effect (PACE) and its variations satisfying some ideas and postulates. Our formula of causal effect uses the idea of the total variation of a function integrated with probability theory. The probabilistic part is the natural availability of changing an exposure values given some variables. These variables interfere with the effect of the exposure on a given outcome. PACE has a parameter $d$ determining the degree of considering the natural availability of changing the exposure values. The lower values of $d$ refer to the scenarios for which rare cases are important. In contrast, with the higher values of $d$, our framework deals with the problems that are in nature probabilistic. Hence, instead of a single value for causal effect, we provide a causal effect vector by discretizing $d$. Further, we introduce the positive and negative PACE to measure the positive and the negative causal changes in the outcome while changing the exposure values. Furthermore, we provide an identifiability criterion for PACE to deal with observational studies. We also address the problem of computing counterfactuals in causal reasoning. We compare our framework to the Pearl, the mutual information, the conditional mutual information, and the Janzing et al. frameworks by investigating several examples.
翻译:在本文中,我们引入了新的因果框架,能够处理概率和非概率问题。事实上,我们提供了一种直接因果公式,称为“概率与因果关系效应”(PACE)及其满足某些想法和假设的变异。我们的因果效应公式使用了与概率理论结合的功能完全变异的概念。概率部分是改变暴露值的自然可得性,这些变量干扰了暴露效应对特定结果的影响。计算机设备行动伙伴关系有一个以美元计算的参数,以确定改变暴露值的自然可得性。美元较低值指的是罕见情况的重要情景。相比之下,与美元较高的值相比,我们的因果效应框架处理的是性质不稳定性的问题。因此,与因果效应的单一价值相比,我们通过离散美元来提供因果矢量。此外,我们引入了正负的因果矢量,以衡量结果中正和负因果变化的程度,同时改变暴露值。美元值的较低值值指的是罕见的假设值。与美元值相比,我们的框架则以相互推理性标准,我们提供了相互推理的推理。