Robert G. Cowell, David Spiegelhalter, Steffen L. Lauritzen et al.|Information science and statistics|1999
Cited by 1.7k
City, University of London
Publishes on Bayesian Modeling and Causal Inference, Bayesian Methods and Mixture Models, Forensic and Genetic Research. 41 papers and 3.2k citations.
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We review recent developments in applying Bayesian probabilistic and statistical ideas to expert systems. Using a real, moderately complex, medical example we illustrate how qualitative and quantitative knowledge can be represented within a directed graphical model, generally known as a belief network in this context. Exact probabilistic inference on individual cases is possible using a general propagation procedure. When data on a series of cases are available, Bayesian statistical techniques can be used for updating the original subjective quantitative inputs, and we present a set of diagnostics for identifying conflicts between the data and the prior specification. A model comparison procedure is explored, and a number of links made with mainstream statistical methods. Details are given on the use of Dirichlet prior distributions for learning about parameters and the process of transforming the original graphical model to a junction tree as the basis for efficient computation.
Abstract Probabilistic expert systems use a directed graphical structure to express conditional independence relationships, and conditional probability tables to summarise quantitative knowledge. We explore the consequences of assuming these probabilities to be parameters, where beliefs about those parameters are updated as data accumulate. A simple approximate Bayesian procedure is shown to be related to those used in ‘unsupervised learning’ and is investigated by simulations and applied to a difficult real example. The procedure has reasonable properties, although for certain missing data configurations the approximations used are clearly somewhat extreme, and further work is required to handle induced dependencies between parameters.
This paper describes a scheme for local computation in conditional Gaussian Bayesian networks that combines the approach of Lauritzen and Jensen (2001) with some elements of Shachter and Kenley (1989). Message passing takes place on an elimination tree structure rather than the more compact (and usual) junction tree of cliques. This yields a local computation scheme in which all calculations involving the continuous variables are performed by manipulating univariate regressions, and hence matrix operations are avoided.