Exploiting partial knowledge to evaluate the average causal effect via an ABC perspective

To evaluate the average causal effect, we propose a method to be used when the variables required to remove confounding are not observed. We consider the case in which the causal structure is known, and there is also some additional partial knowledge. The evaluation is probabilistic, and the partial knowledge may consist of an ordering of some relevant conditional probabilities and/or of the marginal distributions of some variables. A simple way to integrate such additional information is to adopt an approximate Bayesian computation perspective to derive an approximate posterior distribution for the average causal effect. We experimentally evaluate our methodology through an example from the literature, and we compare the results with the exact evaluation of the average causal effect.