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Глава 8. Контрфактивные суждения: глубинный анализ миров, которые могли бы существовать
Annotated Bibliography
The definition of counterfactuals as derivatives of structural equations was introduced by Balke and Pearl (1994a, 1994b) and was used to estimate probabilities of causation in legal settings. The relationships between this framework and those developed by Rubin and Lewis are discussed at length in Pearl (2000, Chapter 7), where they are shown to be logically equivalent; a problem solved in one framework would yield the same solution in another.
Recent books in social science (e.g., Morgan and Winship, 2015) and in health science (e.g., VanderWeele, 2015) are taking the hybrid, graph-counterfactual approach pursued in our book.
The section on linear counterfactuals is based on Pearl (2009, pp. 389–391), which also provides the solution to the problem posed in note 12. Our discussion of ETT is based on Shpitser and Pearl (2009). Legal questions of attribution, as well as probabilities of causation, are discussed at length in Greenland (1999), who pioneered the counterfactual approach to such questions. Our treatment of PN, PS, and PNS is based on Tian and Pearl (2000) and Pearl (2009, Chapter 9). A gentle approach to counterfactual attribution, including a tool kit for estimation, is given in Pearl, Glymour, and Jewell (2016). An advanced formal treatment of actual causation can be found in Halpern (2016).
Matching techniques for estimating causal effects are used routinely by potential outcome researchers (Sekhon, 2007), though they usually ignore the pitfalls shown in our education-experience-salary example. My realization that missing-data problems should be viewed in the context of causal modeling was formed through the analysis of Mohan and Pearl (2014).
Cowles (2016) and Reid (1998) tell the story of Neyman’s tumultuous years in London, including the anecdote about Fisher and the wooden models. Greiner (2008) is a long and substantive introduction to “but-for” causation in the law. Allen (2003), Stott et al. (2013), Trenberth (2012), and Hannart et al. (2016) address the problem of attribution of weather events to climate change, and Hannart in particular invokes the ideas of necessary and sufficient probability, which bring more clarity to the subject.
References
Allen, M. (2003). Liability for climate change. Nature 421: 891–892. Balke, A., and Pearl, J. (1994a). Counterfactual probabilities: Computational methods, bounds, and applications. In Uncertainty in Artificial Intelligence 10 (R. L. de Mantaras and D. Poole, eds.). Morgan Kaufmann, San Mateo, CA, 46–54.
Balke, A., and Pearl, J. (1994b). Probabilistic evaluation of counterfactual queries. In Proceedings of the Twelfth National Conference on Artificial Intelligence, vol. 1. MIT Press, Menlo Park, CA, 230–237.
Cowles, M. (2016). Statistics in Psychology: An Historical Perspective. 2nd ed. Routledge, New York, NY.
Duncan, O. (1975). Introduction to Structural Equation Models. Academic Press, New York, NY.
Freedman, D. (1987). As others see us: A case study in path analysis (with discussion). Journal of Educational Statistics 12: 101–223. Greenland, S. (1999). Relation of probability of causation, relative risk, and doubling dose: A methodologic error that has become a social problem. American Journal of Public Health 89: 1166–1169. Greiner, D. J. (2008). Causal inference in civil rights litigation. Harvard Law Review 81: 533–598.
