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dc.contributor.authorWeisse, Andrea Y*
dc.contributor.authorMiddleton, Richard H*
dc.contributor.authorHuisinga, Wilhelm*
dc.date.accessioned2010-11-19T11:27:27Z
dc.date.available2010-11-19T11:27:27Z
dc.date.issued2010-10-28
dc.identifier.issnhttp://dx.doi.org/10.1186/1752-0509-4-144
dc.identifier.urihttp://hdl.handle.net/10147/115927
dc.description.abstractAbstract 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 of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.
dc.language.isoenen
dc.subjectSTATISTICSen
dc.subject.otherPROBABILITYen
dc.subject.otherMATHEMATICAL MODELSen
dc.titleQuantifying uncertainty, variability and likelihood for ordinary differential equation modelsen
dc.typeArticleen
dc.language.rfc3066en
dc.rights.holderWeisse et al.; licensee BioMed Central Ltd.
dc.description.statusPeer Reviewed
dc.date.updated2010-11-17T13:37:44Z
refterms.dateFOA2018-08-22T09:58:42Z
html.description.abstractAbstract 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 of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.


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