declarative representation of uncertainty in mathematical models声明式表示的数学模型的不确定性.pdfVIP

Declarative Representation of Uncertainty in Mathematical Models 1 1 1,2 Andrew K. Miller *, Randall D. Britten , Poul M. F. Nielsen 1 Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand, 2 Department of Engineering Science, Faculty of Engineering, University of Auckland, Auckland, New Zealand Abstract An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Langu