Graphical Markov Models, Structural Equation Models, and Related Models of Multivariate Dependence: Structure, Equivalence, Synthesis, and Extensions

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DMS 9704516 Graphical Markov Models, Structural Equation Models, and Related Models of Multivariate Dependence: Structure, Equivalence, Synthesis, and Extensions. Steen A. Andersson Indiana University (together with David Madigan, Michael. D. Perlman, and Thomas. S. Richardson, University of Washington) ABSTRACT Graphical Markov models (GMM) and the closely related structural equation models (SEM) use graphs (= path diagrams), either undirected, directed, or mixed, to represent multivariate dependencies among stochastic variables in an economical and computationally efficient manner. A GMM or SEM is constructed by specifying local dependencies 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 dependencies by means of the global structure of the graph. Nonetheless, the local specification permits efficiencies in modeling, inference, and probabilistic calculations. This research involves the development of more complex and comprehensive classes of GMMs and SEMs, determination of the mathematical structure of these (extremely vast) classes, and the development of more efficient statistical and computational algorithms for the discovery and analysis of appropriate models within these classes for specific real-world applications. Among their many applications, GMMs have become prevalent in statistical science for the analysis of categorical data in contingency tables, for the modeling of spatially-dependent processes such as the spread of epidemics in human and animal populations, and for the development of early warning systems for severe weather conditions; in computer science (as Bayesian networks) for information processing and retrieval, for robotics, computer vision, and pattern recognition, for the debugging of complex programs (such as Windows 95), and for the representation of expert systems for medical diagnosis; and in decision science (as influence diagrams) as models for information flow and control and for combining the opinions of many decision-makers. SEMs have long been used in fields such as genetics, sociology, econometrics, and psychometrics as networks for representing the structure of complex causal systems. A crucial feature of all these models is that they are designed for fast computational implementation, thereby facilitating the development of software that can "reason" about real world problems. Related Websites: LA Times Article, October 1996 http://www.hugin.dk/lat-bn.html (Hosted by Hugin Website) Microsoft trouble-shooting systems, employing GMMs http://www.microsoft.com/support/tshooters.htm Lockheed News Release describing application of GMMs in Unmanned Underwater Vehicles. http://www.lmsc.lockheed.com/newsbureau/pressreleases/9604.html Air Force Institute of Technology Bayesian Network Page http://www.afit.af.mil/Schools/EN/ENG/LABS/AI/BayesianNetworks Website describing a GMM for forecasting severe weather in NE Colorado http://www.lis.pitt.edu/~dsl/hailfinder/