Graphical modelling and Bayesian structural learning
Peter Green, University of Technology, Sydney (UTS), Australia and University of Bristol, UK
Conditional independence is key to understanding the structure of multivariate distributions and multivariate data. Graphical modelling provides a rigorous formalism for encoding, visualising and reasoning with conditional independence assumptions, and thus provides tools for assessing structure in data and delivering inferences in graphical form – this is the goal of structural learning. In this lecture, I will review the role of graphical representations of conditional independence in modelling and inference for multivariate data, and their interpretation as a description of structure in the modelled system. I will go on to discuss the state of the art in Bayesian approaches to structural learning: how can we formulate priors, what can we hope to infer (and on what scale and to what degree of approximation), and how should such inferences be interpreted? Decomposable graphs, trees, forests and directed acyclic graphs will all be considered.