Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems

Lambert, Ben; Lei, Chon Lok; Robinson, Martin; Clerx, Michael; Creswell, Richard; Ghosh, Sanmitra; Tavener, Simon; Gavaghan, David J.

Abstract

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes 'random' latent factors affect the system in the ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises owing only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.

Citation

Lambert, B., Lei, C. L., Robinson, M., Clerx, M., Creswell, R., Ghosh, S., …Gavaghan, D. J. (2023). Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems. Journal of the Royal Society. Interface, 20(199), 20220725. https://doi.org/10.1098/rsif.2022.0725

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2023
• Online Publication Date: Feb 22, 2023
• Publication Date: Feb 22, 2023
• Deposit Date: Apr 6, 2023
• Publicly Available Date: Apr 18, 2023
• Journal: Journal of The Royal Society Interface
• Print ISSN: 1742-5689
• Electronic ISSN: 1742-5662
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 199
• Pages: 20220725
• DOI: https://doi.org/10.1098/rsif.2022.0725
• Keywords: Biomathematics, systems biology, computational biology, inference, Bayesian statistics, Fisher information, ordinary differential equations, autocorrelation, measurement error
• Public URL: https://nottingham-repository.worktribe.com/output/17933966
• Publisher URL: https://royalsocietypublishing.org/doi/10.1098/rsif.2022.0725
• Additional Information: Lambert Ben, Lei Chon Lok, Robinson Martin, Clerx Michael, Creswell Richard, Ghosh Sanmitra, Tavener Simon and Gavaghan David J. 2023 Autocorrelated measurement processes and inference for ordinary differential equation models of biological systemsJ. R. Soc. Interface.202022072520220725 http://doi.org/10.1098/rsif.2022.0725