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

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. F...

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Autores principales: Lambert, Ben, Lei, Chon Lok, Robinson, Martin, Clerx, Michael, Creswell, Richard, Ghosh, Sanmitra, Tavener, Simon, Gavaghan, David J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9943878/
http://dx.doi.org/10.1098/rsif.2022.0725
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author Lambert, Ben
Lei, Chon Lok
Robinson, Martin
Clerx, Michael
Creswell, Richard
Ghosh, Sanmitra
Tavener, Simon
Gavaghan, David J.
author_facet Lambert, Ben
Lei, Chon Lok
Robinson, Martin
Clerx, Michael
Creswell, Richard
Ghosh, Sanmitra
Tavener, Simon
Gavaghan, David J.
author_sort Lambert, Ben
collection PubMed
description 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.
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spelling pubmed-99438782023-02-23 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. J R Soc Interface Life Sciences–Mathematics interface 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. The Royal Society 2023-02-22 /pmc/articles/PMC9943878/ http://dx.doi.org/10.1098/rsif.2022.0725 Text en © 2023 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Life Sciences–Mathematics interface
Lambert, Ben
Lei, Chon Lok
Robinson, Martin
Clerx, Michael
Creswell, Richard
Ghosh, Sanmitra
Tavener, Simon
Gavaghan, David J.
Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title_full Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title_fullStr Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title_full_unstemmed Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title_short Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
title_sort autocorrelated measurement processes and inference for ordinary differential equation models of biological systems
topic Life Sciences–Mathematics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9943878/
http://dx.doi.org/10.1098/rsif.2022.0725
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