Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem

Authors

  • Daniel J. Lawson,

    Corresponding author
    1. Biomathematics and Statistics Scotland James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK
    • Phone: +44-117-928-7990
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  • Grietje Holtrop,

    1. Biomathematics and Statistics Scotland James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK
    2. Rowett Institute of Nutrition and Health at the University of Aberdeen, Bucksburn, Aberdeen, AB21 9SB, Scotland, UK
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  • Harry Flint

    1. Rowett Institute of Nutrition and Health at the University of Aberdeen, Bucksburn, Aberdeen, AB21 9SB, Scotland, UK
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Abstract

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally.

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