Stable Bayesian Parameter Estimation for Biological Dynamical Systems

Abstract

The estimation of kinetic rate constants plays a key role for the development of dynamical models in systems biology. Bayesian inference addresses the issues of noise modelling and quantification of parameter uncertainty. However, current approximate inference techniques suffer from well-known degeneracy and instability problems. We propose a novel Bayesian inference technique to estimate parameters of biological dynamical systems in a convergent and stable way. Our approximation is based on sequential Monte Carlo resampling of belief states according to clusters of particles. The resulting implicit partitions of the parameter space keep the density of samples high in the most informative regions. The method yields two highly desirable results: sample degeneracy is avoided by preventive resampling, while modal instability is contrasted by particle clustering. We have tested our approach on the double Goodwin model. As we show, our strategy improves the stability compared to current methods: at the same computational cost, it is successful in maintaining the required modes where standard approaches systematically fail. Moreover, our strategy suggests regions of interest in the parameter space which cannot be identified by traditional resampling schemes. We expect such improvements to open the way for a better understanding of the dynamical behaviors of nonlinear systems in computational science and engineering.