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June, 1989 Influence Diagrams for Statistical Modelling
J. Q. Smith
Ann. Statist. 17(2): 654-672 (June, 1989). DOI: 10.1214/aos/1176347132

Abstract

A directed graph with identified nodes is defined to represent a set of conditional independence (c.i.) statements. It is shown how new c.i. statements can be read from the graph of an influence diagram and results of Howard and Matheson are rigorised and generalized. A new decomposition theorem, analogous to Kiiveri, Speed and Carlin and requiring no positivity condition, is proved. Connections between influence diagrams and Markov field networks are made explicit. Because all results depend on only three properties of c.i., the theorems proved here can be restated as theorems about other structures like second order processes.

Citation

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J. Q. Smith. "Influence Diagrams for Statistical Modelling." Ann. Statist. 17 (2) 654 - 672, June, 1989. https://doi.org/10.1214/aos/1176347132

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0687.62004
MathSciNet: MR994257
Digital Object Identifier: 10.1214/aos/1176347132

Subjects:
Primary: 62A99
Secondary: 62A15

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • June, 1989
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