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Bayesian inversion of a diffusion model with application to biology
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become chall...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8257546/ https://www.ncbi.nlm.nih.gov/pubmed/34226951 http://dx.doi.org/10.1007/s00285-021-01621-2 |
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author | Croix, Jean-Charles Durrande, Nicolas Alvarez, Mauricio A. |
author_facet | Croix, Jean-Charles Durrande, Nicolas Alvarez, Mauricio A. |
author_sort | Croix, Jean-Charles |
collection | PubMed |
description | A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging or ill-posed. In this work, a linear parabolic equation is considered as a model for protein transcription from MRNA. The objective is to estimate jointly the differential operator coefficients, namely the rates of diffusion and self-regulation, as well as a functional source. The recent Bayesian methodology for infinite dimensional inverse problems is applied, providing a unique posterior distribution on the parameter space continuous in the data. This posterior is then summarized using a Maximum a Posteriori estimator. Finally, the theoretical solution is illustrated using a state-of-the-art MCMC algorithm adapted to this non-Gaussian setting. |
format | Online Article Text |
id | pubmed-8257546 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-82575462021-07-09 Bayesian inversion of a diffusion model with application to biology Croix, Jean-Charles Durrande, Nicolas Alvarez, Mauricio A. J Math Biol Article A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging or ill-posed. In this work, a linear parabolic equation is considered as a model for protein transcription from MRNA. The objective is to estimate jointly the differential operator coefficients, namely the rates of diffusion and self-regulation, as well as a functional source. The recent Bayesian methodology for infinite dimensional inverse problems is applied, providing a unique posterior distribution on the parameter space continuous in the data. This posterior is then summarized using a Maximum a Posteriori estimator. Finally, the theoretical solution is illustrated using a state-of-the-art MCMC algorithm adapted to this non-Gaussian setting. Springer Berlin Heidelberg 2021-07-06 2021 /pmc/articles/PMC8257546/ /pubmed/34226951 http://dx.doi.org/10.1007/s00285-021-01621-2 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Croix, Jean-Charles Durrande, Nicolas Alvarez, Mauricio A. Bayesian inversion of a diffusion model with application to biology |
title | Bayesian inversion of a diffusion model with application to biology |
title_full | Bayesian inversion of a diffusion model with application to biology |
title_fullStr | Bayesian inversion of a diffusion model with application to biology |
title_full_unstemmed | Bayesian inversion of a diffusion model with application to biology |
title_short | Bayesian inversion of a diffusion model with application to biology |
title_sort | bayesian inversion of a diffusion model with application to biology |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8257546/ https://www.ncbi.nlm.nih.gov/pubmed/34226951 http://dx.doi.org/10.1007/s00285-021-01621-2 |
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