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.
|Translated title of the contribution||Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem|
|Pages (from-to)||543 - 556|
|Number of pages||14|
|Volume||53, issue 4|
|Publication status||Published - Jul 2011|