What is the difference between causal models and directed graphical models? What is the difference between causal relationships and directed probabilistic relationships? More concretely, what would you put in the interface of a DirectedProbabilisticModel class, and what in a CausalModel class? Would one inherit from the other?
There are two types of causal model: interventional models and counterfactual models. All directed graphical models can reason observationally. An interventional model is a directed graphical model that can reason with observational and interventional evidence. A counterfactual model can reason with observational, interventional, and counterfactual evidence (interventions whose source is inferences within the model).
In a private email a couple years ago, Pearl wrote me that:
By definition, a model is a list of assumptions, and assumptions are never "known to be true". They may be substantiated by theory, or data, or experiments. But their position in the hierarchy is determined by what they claim, not by where they came from.