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Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics

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Abstract

This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over the associated moral graph. Principles of local computation are outlined for the graphical models, and an algorithm for implementing such computation over the junction tree is described. The approach is illustrated with two examples. The first concerns sales forecasting using a multivariate dynamic linear model. The second concerns inference for the error variance matrices of the model for sales, and illustrates the generality of our geometric approach by treating the matrices directly as random objects. The examples are implemented using a freely available set of object-oriented programming tools for Bayes linear local computation and graphical diagnostic display.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, Science Laboratories,South Road, DH1 3LE, Durham, United Kingdom

    M. Goldstein

  2. Department of Statistics, University of Newcastle, NE1 7RU, Newcastle upon Tyne, United Kingdom

    D. J. Wilkinson

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  1. M. Goldstein
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  2. D. J. Wilkinson
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Goldstein, M., Wilkinson, D.J. Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics. Statistics and Computing 10, 311–324 (2000). https://doi.org/10.1023/A:1008977409172

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