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Statistical analysis of ‘probabilities of causation’ using co-variate information. (English) Zbl 1246.03044

Summary: We deal with two problems concering the probabilities of causation defined by J. Pearl [Causality. Models, reasoning, and inference. 2nd revised ed. Cambridge: Cambridge University Press (2009; Zbl 1188.68291)] namely, the probability that one observed event was a necessary (or sufficient, or both) cause of another; one is to derive new bounds, and the other is to provide the covariate selection criteria. J. Tian and J. Pearl [Ann. Math. Artif. Intell. 28, No. 1–4, 287–313 (2000; Zbl 1048.03502)] showed how to bound the probabilities of causation using information from experimental and observational studies, with minimal assumptions about the data-generating process, and identifiable conditions for these probabilities. In this article, we derive narrower bounds using covariate information that is available from those studies. In addition, we propose the conditional monotonicity assumption so as to further narrow the bounds. Moreover, we discuss the covariate selection problem from the viewpoint of the estimation accuracy, and show that selecting a covariate that has a direct effect on an outcome variable cannot always improve the estimation accuracy, which is contrary to the situation in linear regression models. These results provide more accurate information for public policy, legal determination of responsibility and personal decision making.

MSC:

03B48 Probability and inductive logic
62J99 Linear inference, regression
68T27 Logic in artificial intelligence
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