 
Summary: Sequential Monte Carlo Sampling in Hidden Markov Models
of Nonlinear Dynamical Systems $
X. Zeng, M. Anitescu
Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue,
Building 240, Argonne, IL 604394844, U.S.A.
Abstract
We investigate the issue of which state functionals can have their uncertainty estimated
efficiently in dynamical systems with uncertainty. Because of the high dimensionality
and complexity of the problem, sequential Monte Carlo (SMC) methods are used. We
prove that the variance of the SMC method is bounded linearly in the number of time
steps when the proposal distribution is truncated normal distribution. We also show
that for a moderate large number of steps the error produced by approximation of dy
namical systems linearly accumulates on the condition that the logarithm of the density
function of noise is Lipschitz continuous. This finding is significant because the uncer
tainty in many dynamical systems, in particular, in chemical engineering systems that
can be assumed to have this nature. We demonstrate our findings for a simple test case
from chemical engineering. The theoretical findings provide a foundation for the parallel
software SISTOS.
Keywords: State space model, ordinary differential equation, sequential Monte Carlo
methods, chemical process
