Title: Sequential Monte Carlo Parameter Estimation for Differential Equations
Speaker: Andrea Arnold (Case Western Reserve University)
Abstract: A central problem in numerous applications is the estimation of the unknown parameters of a system of differential equations from noisy measurements of some of the states at discrete times. Formulating the parameter estimation problem in a Bayesian statistical framework, we derive a systematic method for defining the innovation term in the time evolution update of particle filter sequential Monte Carlo algorithms based on an estimate of the approximation errors in numerical propagation. More precisely, we propose to carry out the time integration in the evolution step using linear multistep method (LMM) numerical solvers. The choice of LMMs in this context is motivated by the fact that their stability properties are well-known, and good estimates for the accumulating discretization error exist, thereby providing a basis for estimating rigorously the innovation variance. We demonstrate the effectiveness of the resulting algorithm on a test problem with some of the characteristics of the dynamical systems encountered in metabolic models, as well as an application to dynamic PET scan data.