On identifying causal effects

A variety of questions in causal inference can be represented as probability distributions over hypothetical worlds where idealized randomized experiments known as interventions have taken place. Some such questions are really questions of causal effect of a particular intervention, while others are counterfactual and consider results of interventions which violate the state of affairs actually observed. Randomized experiments are expensive and often illegal. It is therefore imperative to find ways of evaluating, or identifying causal effect and counterfactual questions from available information, and causal assumptions. In this paper, we review the state of the art in identification of causal effects and related counterfactual quantities in the framework of graphical causal models, a formalism where a causal domain of interest is represented by directed acyclic graphs with vertices representing variables of interest, and arrows representing direct causal influences