  We describe and contrast two distinct problem areas for statistical
causality: studying the likely effects of an intervention ("effects of
causes"), and studying whether there is a causal link between the observed
exposure and outcome in an individual case ("causes of effects"). For each of
these, we introduce and compare various formal frameworks that have been
proposed for that purpose, including the decision-theoretic approach,
structural equations, structural and stochastic causal models, and potential
outcomes. It is argued that counterfactual concepts are unnecessary for
studying effects of causes, but are needed for analysing causes of effects.
They are however subject to a degree of arbitrariness, which can be reduced,
though not in general eliminated, by taking account of additional structure in
the problem.
