Causes of effects via a Bayesian model selection procedure

In causal inference, and specifically in the causes-of-effects problem, one is interested in how to use statistical evidence to understand causation in an individual case, and in particular how to assess the so-called probability of causation. The answer involves the use of potential responses, which describe what would have happened to the outcome if we had observed a different value for the exposure. However, even given the best possible statistical evidence for the association between exposure and outcome, we can typically only provide bounds for the probability of causation. Dawid and his colleagues highlighted some fundamental conditions, namely exogeneity, comparability and sufficiency, that are required to obtain such bounds from experimental data. The aim of the present paper is to provide methods to find, in specific cases, the best subsample of the reference data set to satisfy these requirements. For this, we introduce a new variable, expressing the preference whether or not to be exposed, and we set the question up as a model selection problem. The best model is selected by using the marginal probability of the responses and a suitable prior over the model space. An application in the educational field is presented.