We address the problem of integrating data from multiple, possibly biased,
observational and interventional studies, to eventually compute counterfactuals
in structural causal models. We start from the case of a single observational
dataset affected by a selection bias. We show that the likelihood of the
available data has no local maxima. This enables us to use the causal
expectation-maximisation scheme to compute approximate bounds for partially
identifiable counterfactual queries, which are the focus of this paper. We then
show how the same approach can solve the general case of multiple datasets, no
matter whether interventional or observational, biased or unbiased, by
remapping it into the former one via graphical transformations. Systematic
numerical experiments and a case study on palliative care show the
effectiveness and accuracy of our approach, while hinting at the benefits of
integrating heterogeneous data to get informative bounds in case of partial
identifiability.

本文介绍一种方法，通过数据整合和建立结构性因果模型，在不同条件下解决由选择偏差引起的局部统计问题，并针对数据集的部分可识别性问题提出了一种逼近计算方法。通过系统的实验验证和实例研究，证明了这种方法的可行性和准确性，并揭示了数据整合对于信息界的提高具有积极的作用。