Prediction, Intervention and Discovery
This talk will focus on topics related to Bayesian networks, a type of graphical model. In general, a graphical model has a qualitative part, a graph over a set of variables, and a quantitative part, a joint distribution over the set of variables. The qualitative part represents a set of independence constraints true of the joint distribution. In the case of a Bayesian network the graph is a directed acyclic graph. The class of Bayesian network models is a rich class of models which subsumes many standard classes of statistical models including regression models, factor analytic models, and recursive structural equation models. I will discuss various qualitative and quantitative aspects of the Bayesian network framework and describe some recent work on the model selection problem for Bayesian networks. As with structural equation models, the graph of a Bayesian network can also be interpreted causally. This interpretation allows one to address the problem of predicting the effects of interventions. In addition I will discuss a variety of assumptions, some of which are commonly made by statisticians, that allow for the possibility of discovering causal relationships from observational data.