University of Washington - Department of Statistics
Multivariate Analysis & Graphical Models of Association (MAGMA 4) Workshop
Graphical Markov models represent statistical dependencies by combining two simple yet powerful mathematical concepts: graphs and conditional independence. A graphical Markov model is constructed by specifying local dependencies for each node of the graph in terms of its immediate neighbors, yet can represent a highly varied and complex system of multivariate dependencies by means of the global structure of the graph. Nonetheless, the local specification permits efficiencies in modelling, statistical inference, and probabilistic calculations.
In statistics, the systematic development of graphical Markov models for both categorical and continuous data accelerated rapidly in the 1970s, beginning with work on decomposable log-linear models for contingency tables, recursive systems of simultaneous linear equations, and nearest-neighbor models in spatial statistics and image analysis. At the same time, separate but convergent developments of these ideas occurred in computer science, decision analysis, and philosophy, where graphical Markov models have been called influence diagrams, belief networks, or Bayesian networks, and have been used for the construction of expert systems and for causal modelling.