Establishing cause-effect relationships is fundamental to progress of empirical science. A general mathematical theory of causation which supports human causal intuitions is thus of utmost importance for formalizing and perhaps one day automating scientific inquiry. This tutorial will describe one such theory of causation, based on graphical models. The tutorial will consist of two parts.

The first part will introduce graphical causal models as vehicles for expressing causal assumptions, and interventions as an operation formalizing the notions of causal effects and counterfactuals. Examples of using this framework to pose and answer practical causal questions in public health will be given. The first part will conclude by giving a general algorithm for identifying causal effects from observational studies, and showing how the so called post-truncation independence constraints in latent variable graphical models can be given an interpretation in terms of such effects.

The second part will discuss a recursive factorization (r-factorization) for latent variable graphical models, and show how post-truncation constraints which do not make an appearance in directed acyclic graph (DAG) models are captured by this factorization. A causal interpretation of this factorization will be given. The second part will conclude by giving some notable examples of such models, including testably distinct models which agree on all conditional independences, and models with a graph fully specified by a single post-truncation independence.