Bayesian inversion of a diffusion model with application to biology
| Autor: | Jean-Charles Croix, Nicolas Durrande, Mauricio A. Álvarez |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Diffusion equation
Dynamical systems theory Bayesian probability Posterior probability Functional MCMC Gaussian processes 010103 numerical & computational mathematics 01 natural sciences Article Diffusion 010104 statistics & probability symbols.namesake Applied mathematics 62G05 0101 mathematics Gaussian process Biology Partial differential equation Mathematical model Applied Mathematics Bayesian inverse problems Bayes Theorem Inverse problem Models Theoretical Agricultural and Biological Sciences (miscellaneous) 35R30 Modeling and Simulation 62P10 symbols 62F15 Algorithms |
| Zdroj: | Croix, J C, Durrande, N & Alvarez, M A 2021, ' Bayesian inversion of a diffusion model with application to biology ', Journal of Mathematical Biology, vol. 83, no. 2, 13 . https://doi.org/10.1007/s00285-021-01621-2 Journal of Mathematical Biology |
| DOI: | 10.1007/s00285-021-01621-2 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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