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Research Article
Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem
Article first published online: 16 JUN 2011
DOI: 10.1002/bimj.201000250
Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-4036/asset/cover.gif?v=1&s=44244e92ebd601b98ef501afeb3e1ab7a016a4c3 "Biometrical Journal")
Additional Information
How to Cite
Lawson, D. J., Holtrop, G. and Flint, H. (2011), Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem. Biom. J., 53: 543–556. doi: 10.1002/bimj.201000250
Publication History
- Issue published online: 30 JUN 2011
- Article first published online: 16 JUN 2011
- Manuscript Accepted: 2 MAY 2011
- Manuscript Revised: 7 APR 2011
- Manuscript Received: 9 DEC 2010
Funded by
- Scottish Government Rural and Environment Research and Analysis Directorate (RERAD)
Keywords:
- Bacteria;
- Convergence;
- Ecology;
- Hierarchical model;
- Process model
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.