Probabilistic networks and expert systems.

*(English)*Zbl 0937.68121
Statistics for Engineering and Information Science. New York, NY: Springer. xii, 321 p. (1999).

This book is the result of the authors’ investigations on the problem of potential connection between graphical modeling in contingency tables and the type of diagrams being used to represent qualitative knowledge in expert systems. Being as specialists in various knowledge domains the authors have common interests in the area of application in probabilistic networks for expert systems. Fully probabilistic approach to construction of expert systems has steadily gained acceptance in 1988 after publication the work [J. Pearl, Probabilistic Inference in Intelligent Systems. Morgan Kaufmann, San Mateo, California]. It is noted that probabilistic approach practical usage to the soling of higher dimensions problems can be successful if will be find some way of introducing “modularity”, so enabling a large and complex model, and its associated calculations, to be split up into small manageable pieces. The best way to do this turns out to be through the imposition of meaningful simplifying conditional independence assumptions. These, in turn, can be expressed by means of a powerful and appealing graphical representation, and the resulting networks and often termed Bayesian networks. In spite of the fact that the range of researches now involved in this field from Computer Science, Engineering, Statistics and the Social Sciences the authors believe that there is still a particular contribution to be made from the statistical perspective emphasizing the generality of the concepts and attempting to place them on a rigorous footing. After necessary material from logic and probability theory the authors pass to building and using probabilistic networks, graph theory and Markov properties on graphs, discrete networks, Gaussian and mixed discrete-Gaussian networks and discrete multistage decision networks. Detailed numerical examples are given. Conclusive chapters present some exact and approximate methods for learning about unknown probabilities in a network, for both complete and incomplete data; and give an important issue of criticizing a network in the light of observed data by establishing systems of monitors to identify failings of various aspects of the model structure. The Chapter 11 deals with some aspects of the currently active topic of learning about the graphical structure of a problem from data. Each chapter contains a guide to further reading. The book concludes with three appendices: on Bayesian conjugate analysis of discrete data, on stochastic simulation and Gibbs sampling, and on information and software available on the World Wide Web. The reviewing book will be interested to specialists on the elaboration and usage of expert systems in the applications to various scientific disciplines.

Reviewer: S.G.Valeev (Ul’yanovsk)