### APPROXIMATE BAYESIAN PARAMETER INFERENCE FOR DYNAMICAL SYSTEMS IN SYSTEMS BIOLOGY

#### Abstract

A b s t r a c t: This paper proposes to use approximate instead of exact stochastic simulation algorithms for approximate Bayesian parameter inference of dynamical systems in systems biology. It first presents the mathematical framework for the description of systems biology models, especially from the aspect of a stochastic formulation as opposed to deterministic model formulations based on the law of mass action. In contrast to maximum likelihood methods for parameter inference, approximate inference methodsare presented which are based on sampling parameters from a known prior probability distribution, which gradually evolves tward a posterior distribution, through the comparison of simulated data from the model to a given data set of measurements. The paper then discusses the simulation process, where an overview is given of the different exact and approximate methods for stochastic simulation and their improvements that we propose. The exact and approximate simulators are implemented and used within approximate Bayesian parameter inference methods. Our evaluation of these methods on two tasks of parameter estimation in two different models shows that equally good results are obtained much faster when using approximate simulation as compared to using exact simulation.

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DOI: http://dx.doi.org/10.20903/csnmbs.masa.2010.31.1-2.24

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