Simulating counterfactuals

A counterfactual distribution is the probability distribution of a random variable under a hypothetical scenario that differs from the observed reality. "What would have been the outcome for this individual if they had received a different treatment?" is an example of a counterfactual question. Here the personal data of the individual constitute the evidence that specifies the observed reality, and the interest lies in the distribution of the outcome under a hypothetical treatment. Counterfactual questions belong to the third and highest level in the causal hierarchy (Shpitser and Pearl, 2008) and are in general more difficult than associational (first level) or interventional (second level) questions. Algorithms for checking the identifiability of counterfactual queries from observational and experimental data have been developed (Shpitser and Pearl, 2007; Shpitser and Sherman, 2018; Correa et al., 2021) and implemented (Tikka, 2022).