Andrea Arnold
Department of Mathematics, Case Western Reserve University
Sequential Monte Carlo particle filtering for parameter estimation
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.