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

DMS 9704573 图形马尔可夫模型，结构方程模型，和 多元依赖的相关模型：结构，等价性， 合成和扩展。 大卫梅迪根，迈克尔。D.帕尔曼和托马斯。S. 理查森 华盛顿大学（与Steen。A.安德森，印第安纳州大学） 摘要 图马尔可夫模型（GMM）和密切相关的结构 方程模型（SEM）使用图表（=路径图），或者 无向、有向或混合，以表示多变量 在一个经济的随机变量之间的依赖性， 高效的计算方式。GMM或SEM通过以下方式构建： 指定每个变量的局部依赖关系（= 图）在其近邻，父母，或两者，但 可以代表一个高度变化和复杂的多变量系统 依赖关系通过图的全局结构。 尽管如此，当地规范允许在以下方面提高效率： 建模、推理和概率计算。这项研究涉及更复杂和全面的类的发展，GSPs和SEM，确定的数学结构， 这些（极其庞大的）类，以及更多的发展 有效的统计和计算算法， 发现和分析这些类别中的适当模型，以用于特定的实际应用。 在它们的许多应用中，甘精胰岛素已在 分类数据分析的统计科学 列联表，用于空间相关的 人类和动物中流行病的传播等过程 和发展预警系统 用于恶劣的天气条件;在计算机科学中（如贝叶斯 用于信息处理和检索，用于机器人，计算机视觉和模式识别，用于调试 复杂的程序（如Windows 95），以及用于医疗诊断的经验系统的表示;以及在决策科学中（如影响图）作为信息流和控制的模型，以及用于结合许多决策者的意见。SEM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，作为用于表示 复杂的因果系统所有这些模型的一个关键特征是 它们是为快速计算实现而设计的，从而促进了能够“推理”真实的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网站提供） 微软故障排除系统，采用GARNET http://www.microsoft.com/support/tshooters.htm 洛克希德公司新闻稿描述了GST-T的应用 无人水下航行器 http://www.lmsc.lockheed.com/newsbureau/pressreleases/9604.html 空军技术学院贝叶斯网络页面 http://www.afit.af.mil/Schools/EN/ENG/LABS/AI/BayesianNetworks 描述GMM用于预测恶劣天气的网站 东北部科罗拉多http://www.lis.pitt.edu/~dsl/hailfinder/

DMS 9704573 Graphical Markov Models, Structural Equation Models, and Related Models of Multivariate Dependence: Structure, Equivalence, Synthesis, and Extensions. David Madigan, Michael. D. Perlman, and Thomas. S. Richardson University of Washington (together with Steen. A. Andersson, Indiana University) 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 exp ert 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/