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

图形马尔可夫模型，结构方程模型，和相关的模型多元依赖：结构，等价，综合，和扩展。Steen A. Andersson印第安纳大学(与David Madigan， Michael。帕尔曼和托马斯。图形马尔可夫模型（GMM）和与其密切相关的结构方程模型（SEM）使用无向、有向或混合的图（=路径图），以经济和计算效率高的方式表示随机变量之间的多变量依赖关系。GMM或SEM是通过根据其近邻、父节点或两者指定每个变量（=图的节点）的局部依赖关系来构建的，但可以通过图的全局结构表示高度变化和复杂的多元依赖系统。尽管如此，本地规范允许在建模、推理和概率计算方面提高效率。这项研究包括开发更复杂和全面的gmm和sem类，确定这些（极其庞大的）类的数学结构，以及开发更有效的统计和计算算法，以便在这些类中发现和分析适用于特定现实世界应用的适当模型。在其众多应用中，gmm已在统计科学中变得普遍，用于分析列联表中的分类数据，用于模拟依赖空间的过程，例如流行病在人类和动物种群中的传播，以及用于开发恶劣天气条件的早期预警系统；在计算机科学（如贝叶斯网络）中，用于信息处理和检索，用于机器人，计算机视觉和模式识别，用于复杂程序的调试（如Windows 95），以及用于医学诊断的专家系统的表示；在决策科学中（如影响图），作为信息流和控制的模型，以及结合许多决策者的意见的模型。sem长期以来被用于遗传学、社会学、计量经济学和心理测量学等领域，作为表示复杂因果系统结构的网络。所有这些模型的一个关键特征是，它们都是为快速计算实现而设计的，从而促进了能够“推理”现实世界问题的软件的开发。相关网站：洛杉矶时报文章，1996年10月http://www.hugin.dk/lat-bn.html（由Hugin网站主持）微软故障排除系统，采用GMMs http://www.microsoft.com/support/tshooters.htm洛克希德新闻发布描述GMMs在无人水下航行器中的应用。http://www.lmsc.lockheed.com/newsbureau/pressreleases/9604.html空军理工学院贝叶斯网络页面http://www.afit.af.mil/Schools/EN/ENG/LABS/AI/BayesianNetworks网站描述了一个用于预测科罗拉多州东北部恶劣天气的GMM http://www.lis.pitt.edu/~dsl/hailfinder/

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/