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June 2023 Bayes Linear Bayes Networks with an Application to Prognostic Indices
Wael A. J. Al-Taie, Malcolm Farrow
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Bayesian Anal. 18(2): 437-463 (June 2023). DOI: 10.1214/22-BA1314


Bayes linear kinematics and Bayes linear Bayes graphical models provide an extension of Bayes linear methods so that full conditional updates may be combined with Bayes linear belief adjustment. The use of Bayes linear kinematics eliminates the problem of non-commutativity which was observed in earlier work involving moment-based belief updates. In this paper we describe this approach and investigate its application to the rapid computation of prognostic index values in survival when a patient’s values may only be available for a subset of covariates. We consider the use of covariates of various kinds and introduce the use of non-conjugate marginal updates. We apply the technique to an example concerning patients with non-Hodgkin’s lymphoma, in which we treat the linear predictor of the lifetime distribution as a latent variable and use its expectation, given whatever covariates are available, as a prognostic index.


The authors thank the three reviewers for their constructive comments and suggestions which have helped to improve the paper.


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Wael A. J. Al-Taie. Malcolm Farrow. "Bayes Linear Bayes Networks with an Application to Prognostic Indices." Bayesian Anal. 18 (2) 437 - 463, June 2023.


Published: June 2023
First available in Project Euclid: 2 May 2022

MathSciNet: MR4578060
Digital Object Identifier: 10.1214/22-BA1314

Keywords: Bayes linear Bayes graphical model , Bayes linear kinematics , missing covariates , prognostic index , Survival analysis

Vol.18 • No. 2 • June 2023
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