Adaptive Approach for Modelling Variability in Pharmacokinetics

Weiße, Andrea Y.; Horenko, Illia; Huisinga, Wilhelm

doi:10.1007/11875741_19

Cited by 6 publications

(5 citation statements)

References 11 publications

(14 reference statements)

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“…For the applications visited in this article, the models proved well behaved enough such that a single component and 10 components respectively for the crosstalk and JAK-STAT systems sufficed for sufficient agreement with the nested sampling and Monte Carlo results. An improvement to the method described here would be to update the number of components automatically with respect to the model behaviour in a manner similar to how Gaussian mixtures can be adaptively chosen in particle based simulation of Liouville-type equations [28] , [29] .…”

Section: Methodsmentioning

confidence: 99%

Model Selection in Systems Biology Depends on Experimental Design

et al. 2014

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Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.

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Section: Methodsmentioning

confidence: 99%

Model Selection in Systems Biology Depends on Experimental Design

et al. 2014

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“…ref. 10). Consequently, if repetitions of the measurement are not advisable or will not improve the result, one should implement statistical aspects into the models under consideration.…”

Section: Introduction Of the Overlap-conceptmentioning

confidence: 93%

“…no constraints, since variances are invariant wrt. that orthogonal basis transformation and hence will not influence the computation of the overlap functional defined in (10). To calculate (7), one needs to model the parameter density π θ .…”

Section: Overlap Notationmentioning

confidence: 99%

Discrimination of dynamical system models for biological and chemical processes

et al. 2007

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In technical chemistry, systems biology and biotechnology, the construction of predictive models has become an essential step in process design and product optimization. Accurate modelling of the reactions requires detailed knowledge about the processes involved. However, when concerned with the development of new products and production techniques for example, this knowledge often is not available due to the lack of experimental data. Thus, when one has to work with a selection of proposed models, the main tasks of early development is to discriminate these models. In this article, a new statistical approach to model discrimination is described that ranks models wrt. the probability with which they reproduce the given data. The article introduces the new approach, discusses its statistical background, presents numerical techniques for its implementation and illustrates the application to examples from biokinetics.

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“…An implementation was the TRAIL (Trapezoid Rule for Adaptive Integration of Liouville dynamics) algorithm, which was first applied to problems of molecular dynamics. In [29] it was also used to describe stochastic uncertainties in macroscopic fields.…”

Section: Solution Strategiesmentioning

confidence: 99%

Adaptive Gaussian particle method for the solution of the Fokker‐Planck equation

Scharpenberg¹,

Lukáčová-Medviová²

2012

Z Angew Math Mech

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The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE) or a deterministic ordinary differential equation (ODE) with stochastic initial values. A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the ODE. The decomposition as well as the propagation is subject to possibly large numerical errors due to the difficulty to control the spatial residual over the whole domain.In this paper a new particle method is derived, which allows a deterministic error control for the resulting probability density. It is based on global optimization and allows an adaption of an efficient surrogate model for the residual estimation. Error controlled uncertainty analysisFor any numerical application knowledge about the accuracy of the applied method is essential. If we simulate a physical system, further knowledge about the effect of uncertainties in the input parameters is vital for the assessment and validation of the results. In [7] it is noted that uncertain input data does not only lead to an uncertain solution but to an uncertain solution error as well.In the following both aspects will be covered for stochastic uncertainties within a system of ordinary differential equa-The ODE itself is considered deterministic, but the initial data is assumed to be uncertain. As shown in [13] this formulation also covers an ODE with stochastic parameters, which are treated as independent and constant additional states.

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Adaptive Approach for Modelling Variability in Pharmacokinetics

Cited by 6 publications

References 11 publications

Model Selection in Systems Biology Depends on Experimental Design

Model Selection in Systems Biology Depends on Experimental Design

Discrimination of dynamical system models for biological and chemical processes

Adaptive Gaussian particle method for the solution of the Fokker‐Planck equation

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