Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs

Andrea  Arnold; Daniela Calvetti; Erkki  Somersalo

doi:10.3934/proc.2015.0075

Article Contents

2015, Volume 2015: 75-84. Doi: 10.3934/proc.2015.0075 open access

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Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs

1.
Department of Mathematics, North Carolina State University, Campus Box 8205, 2311 Stinson Drive, 2108 SAS Hall, Raleigh, NC 27695-8205
2.
Case Western Reserve University, Department of Mathematics and Center for Modelling Integrated Metabolic Systems, 10900 Euclid Avenue, Cleveland, OH 44106
3.
Case Western Reserve University, Department of Mathematics, Applied Mathematics, and Statistics, Cleveland, OH 44106

Received: July 31, 2014

Revised: August 31, 2015

Published: October 2015

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Abstract

Particle filter (PF) sequential Monte Carlo (SMC) methods are very attractive for estimating parameters of time-dependent systems where the data is either not all available at once, or the range of time constants is wide enough to create problems in the numerical time propagation of the states. The need to evolve (and hence integrate) a large number of particles makes PF-based methods computationally challenging, and parallelization is often advocated to speed up computing time. While careful parallelization may indeed improve performance, vectorization of the algorithm on a single processor may result in even larger speedups for certain problems. In this paper we demonstrate how the PF-SMC class of algorithms proposed in [2] can be implemented in both parallel and vectorized computing environments, illustrating the performance with computed examples in MATLAB. In particular, two stiff test problems with different features show that both the size and structure of the problem affect which version of the algorithm is more efficient.

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Mathematics Subject Classification: Primary: 65Y05, 65Y10; Secondary: 62M20, 65L06, 62M05.

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