University of Washington - Department of Statistics
In a graphical Markov model a graph which contains vertices and edges is used to represent the conditional independence structure of a set of probability distributions.
The number of possible independence models grows very rapidly in the number of variables: with four variables there are already 18300 different models. Any class of graphs will only be able to represent a subset of the set of all possible independence models. Consequently, when performing model selection in a given class of graphical models, a modeller is excluding many independence hypotheses from consideration. It is thus important to identify classes of independence models which are likely to arise from data-generating processes. In this talk I will address two specific questions within this general research project:
(1) Which conditional independence hypotheses may arise among a subset of the variables in a generating process, when the remainder are either marginalized over or conditioned on?
(2) Which data-generating processes correspond to chain graph models?
Joint work with Peter Spirtes (1) and Steffen Lauritzen (2).