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Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems. (English) Zbl 1334.65011
Summary: 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 investigate SMC methods where the proposal distribution is computed by maximum likelihood or by a linearization approach. 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 dynamical systems linearly accumulates on the condition that the logarithm of the density function of noise is Lipschitz continuous. This finding is significant because the uncertainty in many dynamical systems, in particular, in chemical engineering systems, 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.
MSC:
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
62D05 Sampling theory, sample surveys
62M05 Markov processes: estimation; hidden Markov models
Software:
ADIC; ADOL-C; CVODES; PETSc; SISTOS; TAO
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