Generalizing Conditional Independence: Nested Markov Models
You are all invited to an exciting seminar at Biostats on Friday, January 24 @ 15:00. Note the slightly different time and room (still on CSS)!
Place: Øster Farimagsgade 5, Room 6, Floor 1, Building 35
Speaker: Thomas S Richardson, Department of Statistics, University of Washington, Seattle
Generalizing Conditional Independence: Nested Markov Models
Abstract
Graphical models based on directed acyclic graphs (DAGs), also known as Bayesian networks, have found application. This stems from their well understood Markov properties and intuitive causal interpretation under the assumption that there are no unmeasured common causes. However, it has also been known for more than 30 years that DAG models with hidden variables give rise to non-parametric (“Verma”) constraints that generalize conditional independence. The nested Markov model is a class of graphical models associated with acyclic graphs containing directed and bidirected edges that encode all of the non-parametric equality constraints implied by DAGs with latent variables. In this talk I will first review the problem of causal identification from DAGs in the presence of hidden variables. This motivates a `fixing’ operation that may be applied to graphs and associated distributions. This operation leads to a simple reformulation of the ID algorithm of Tian & Pearl. I will then show that the fixing operation may be used to define the nested Markov model and the associated global property. I will also describe simple preservation rules for reasoning with such constraints. Finally, (time permitting) I will outline a local property and sketch why this construction is more involved than for ordinary independence models.