Quantifying uncertainty, variability and likelihood for ordinary differential equation models

Andrea Y. Weiße, Richard H. Middleton, Wilhelm Huisinga

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Abstract / Description of output

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.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.Ordinary differential equations (ODEs) are commonly used for modeling biological and biochemical systems. ODE models are often subject to considerable uncertainty and/or variability in both initial conditions and parameters [1-4]. Particularly in the case of nonlinear ODEs, it is essential to have efficient and accurate techniques for analyzing the effects of uncertainty and variability on the dynamical behavior. The effect of variations in the input on model behavior (output), the model sensitivity, can be analyzed in various ways. Most numerical approaches address the problem either by computing local sensitivity indices (partial derivatives of the solution with respect to the input variables) [5,6], by solving the ODE for a statistically large ensemble of random or quasi-random input values [7-9], or by approximating the functional relationship of the input and output [10-12]. When uncertainty can be narrowed down to 'small' perturbations, it is often sufficient to study its effects locally. It is, however, difficult to determine a priori if the uncertainty is small, and in many biological applications
Original languageEnglish
Pages (from-to)144
Number of pages1
JournalBMC Systems Biology
Volume4
DOIs
Publication statusPublished - 2010

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