University of Washington - Department of Statistics
Graphical Markov models (GMM) use graphs, either undirected, directed, or mixed, to represent multivariate dependences among a set of stochastic variables in a visual and computationally efficient manner. GMMs comprise one of the most interdisciplinary topics of contemporary statistical science, with applications arising in a host of areas such as computer science (e.g., expert systems, robotics, data-mining, machine learning), electrical engineering (automatic speech recognition systems,error-correcting codes), genetics (modelling phylogenies and gene-expression data), geophysics (Markov random fields), epidemiology (causal models), econometrics (structural equations), and social science (modelling social networks).
A GMM is usually constructed by specifying local dependences for each variable = node of the graph in terms of its immediate neighbors, parents, or both, yet can represent a highly varied and complex system of multivariate dependences by means of the global structure of the graph. The local specification permits efficiencies in modeling, inference, and probabilistic calculations. Model selection is particularly challenging, however, since the number of possible graphs grows super exponentially with the number of variables.
In the first half of this talk I will review the basic definitions and properties of GMMs. In the second half I will discuss my recent joint paper "A SINful approach to Gaussian graphical model selection" with Mathias Drton, where the Fisher z-transform and Sidak's inequality for correlated normal variables sometimes can be used to greatly simplify the model selection problem.