INTRODUCTION TO NESTED MARKOV MODELS

Graphical models provide a principled way to take advantage of independence constraints for probabilistic and causal modeling, while giving an intuitive graphical description of “qualitative features” useful for these tasks. A popular graphical model, known as a Bayesian network, represents joint distributions by means of a directed acyclic graph (DAG). DAGs provide a natural representation of conditional independence constraints, and also have a simple causal interpretation. When all variables are observed, the associated statistical models have many attractive properties. However, in many practical data analyses unobserved variables may be present. In general, the set of marginal distributions obtained from a DAG model with hidden variables is a much more complicated statistical model: the likelihood of the marginal is often intractable; the model may contain singularities. There are also an infinite number of such models to consider.