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

DMS 9704516图形马尔可夫模型、结构方程模型和多元相关性的相关模型：结构、等价、综合和扩展。史蒂恩·A·安德森印第安纳大学(与大卫·梅迪根，迈克尔)D.帕尔曼和托马斯。S.Richardson，Washington)提出的抽象图形化马尔可夫模型(GMM)和紧密相关的结构方程模型(SEM)使用无向图、有向图或混合图以经济和计算高效的方式表示随机变量之间的多变量相关性。GMM或SEM是通过为每个变量(=图的节点)指定其直接邻居、父代或两者的局部依赖关系来构建的，但也可以通过图的全局结构来表示高度多样和复杂的多变量依赖关系系统。尽管如此，本地规范允许在建模、推理和概率计算中提高效率。这项研究涉及开发更复杂和更全面的GMM和SEM类别，确定这些(极其庞大的)类别的数学结构，以及开发更有效的统计和计算算法，以便在这些类别中发现和分析特定现实世界应用的适当模型。在GMM的众多应用中，GMM已普遍用于统计科学，用于分析列联表中的分类数据，用于对流行病在人和动物种群中的传播等空间相关过程进行建模，并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、机器人学、计算机视觉和模式识别、复杂程序的调试(如Windows 95)，以及用于医疗诊断的专家系统的表示；在决策科学中(作为影响图)，作为信息流和控制的模型，并结合许多决策者的意见。SEMS长期以来一直被用于遗传学、社会学、计量经济学和心理计量学等领域，作为表示复杂因果系统结构的网络。所有这些模型的一个重要特征是，它们都是为快速计算实现而设计的，从而促进了能够对现实世界的问题进行“推理”的软件的开发。相关网站：La Times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GMM http://www.microsoft.com/support/tshooters.htm洛克希德公司描述GMM在无人水下机器人中的应用的新闻稿。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网站描述了一种预报东北科罗拉多州恶劣天气的通用预测模型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/