ABSTRACT
This chapter focuses on statistical contexts where causal inference uses data to inform decisions about actions, for example with a view to public health policies. It considers different approaches to formalizing causal inquiries which, despite subtle differences, all build on a probabilistic graphical representation of the problem at hand. The chapter presents different approaches in order to illustrate the flexibility and representational power of graphical models. It provides brief tour through different causal notations and frameworks introduces common key concepts as well as differences between formal approaches. The complete identification algorithm of I. Shpitser and J. Pearl can be regarded as combining and generalizing these two criteria in the context of causal directed acyclic graphs (DAG). The chapter consider two different approaches to extending DAGs with a view to a causal interpretation. The first adds a particular type of node representing experimental manipulation or intervention. The second approach modifies the semantics of a DAG to obtain a causal DAG.
