Identification and Estimation of ``Causes of Effects'' using Covariate-Mediator Information

In this paper, we deal with the evaluation problem of "causes of effects" (CoE), which focuses on the likelihood that one event was the cause of another. To assess this likelihood, three types of probabilities of causation have been utilized: probability of necessity, probability of sufficiency, and probability of necessity and sufficiency. However, these usually cannot be estimated, even if "effects of causes" (EoC) is estimable from statistical data, regardless of how large the data is. To solve this problem, we propose novel identification conditions for CoE, using an intermediate variable together with covariate information. Additionally, we also propose a new method for estimating CoE that is applicable whenever they are identifiable through the proposed identification conditions.