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Probabilistic causality

机译：概率因果关系

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Necessity and Sufficiency are two of the most important concepts in science. Indeed, they are the basis for establishing causal relationships between factors, variables, etc. In contradistinction to most treatments of causality, we show how to compute the probability that Necessity and Sufficiency obtain. We thus treat probabilistic causality, which is key to Technological Forecasting since we are never dealing with complete knowledge or perfect certainty. This paper shows how decision makers can obtain direct estimates of the probabilities of the Necessity and the Sufficiency of various proposed courses of action and thereby make better decisions with regard to their efficacy. The paper goes beyond typical chi-square analyses that show whether there are significant statistical relationships between two or more variables. Instead, whatever the level of statistical significance, it shows how one can determine the amount or degree of Sufficiency and Necessity that exists between two or more variables. In fact, we show how statistical significance and Sufficiency and Necessity are related. In particular, we show how the correlation coefficient between two variables is a direct function of Sufficiency and Necessity. To do this, we adapt a framework from epidemiology: Predictive Value Theory. Although Predictive Value Theory was originally developed to help physicians make critical decisions, e.g., whether to administer or not to administer a treatment, or to screen or not to screen for say cancer, it is so general that with little modification it applies equally well to decision making in general. By combining probability theory and elementary logic, we show how one can measure directly the Sufficiency and the Necessity of a test from the data that are gathered in a typical application of Predictive Value Theory. The result is not only a better understanding of Predictive Value Theory, but its extended application to decision making in general. Finally, the paper goes beyond traditional Bayesian ways of computing the probability of implication and hence Sufficiency and Necessity.
机译：必要性和充分性是科学中两个最重要的概念。的确，它们是在因素，变量等之间建立因果关系的基础。与大多数因果关系的处理方法相反，我们展示了如何计算必要性和充分性获得的可能性。因此，我们对待概率因果关系，这是技术预测的关键，因为我们从未处理过完整的知识或绝对的确定性。本文展示了决策者如何直接估计各种拟议行动方案的必要性和充分性的概率，从而就其有效性做出更好的决策。本文超越了典型的卡方分析，该分析显示了两个或多个变量之间是否存在显着的统计关系。相反，无论统计显着性水平如何，它显示了人们如何确定两个或多个变量之间存在的充实度和必要性的程度或程度。实际上，我们显示了统计显着性与充分性和必要性之间的关系。特别是，我们展示了两个变量之间的相关系数如何直接满足充足性和必要性。为此，我们采用了流行病学的框架：预测价值理论。尽管预测价值理论最初是为了帮助医生做出关键性决定而开发的，例如，是否进行某种治疗，或者是否进行某种癌症的筛查，但它是如此普遍，以至于几乎没有任何修改，它同样适用于一般的决策。通过将概率论和基本逻辑相结合，我们展示了如何从预测价值理论的典型应用中收集的数据直接测量测试的充分性和必要性。结果不仅可以更好地理解预测价值理论，而且可以将其广泛地应用于决策。最后，本文超越了传统的贝叶斯方法来计算隐含概率，从而计算了充分性和必要性。

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