Quantifying uncertainty, variability and likelihood for ordinary differential equation models
- Background In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study ofBackground In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.…
Author details: | Andrea Y. Weiße, Richard H. Middleton, Wilhelm HuisingaORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-431340 |
DOI: | https://doi.org/10.25932/publishup-43134 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (894) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2020/04/22 |
Publication year: | 2010 |
Publishing institution: | Universität Potsdam |
Release date: | 2020/04/22 |
Tag: | Ordinary Differential Equation model; Unscented Kalman Filter; global sensitivity analysis; joint normal distribution; ordinary differential equation |
Issue: | 894 |
Number of pages: | 12 |
Source: | BMC Systems Biology 4(2010) 144 DOI: 10.1186/1752-0509-4-144 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 57 Biowissenschaften; Biologie / 570 Biowissenschaften; Biologie |
6 Technik, Medizin, angewandte Wissenschaften / 61 Medizin und Gesundheit / 610 Medizin und Gesundheit | |
Peer review: | Referiert |
Publishing method: | Open Access |
License (English): | Creative Commons - Namensnennung 2.0 Generic |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |