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Accelerated Monte Carlo for Optimal Estimation of Time Series

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By casting stochastic optimal estimation of time series in path integral form, one can apply analytical and computational techniques of equilibrium statistical mechanics. In particular, one can use standard or accelerated Monte Carlo methods for smoothing, filtering and/or prediction. Here we demonstrate the applicability and efficiency of generalized (nonlocal) hybrid Monte Carlo and multigrid methods applied to optimal estimation, specifically smoothing. We test these methods on a stochastic diffusion dynamics in a bistable potential. This particular problem has been chosen to illustrate the speedup due to the nonlocal sampling technique, and because there is an available optimal solution which can be used to validate the solution via the hybrid Monte Carlo strategy. In addition to showing that the nonlocal hybrid Monte Carlo is statistically accurate, we demonstrate a significant speedup compared with other strategies, thus making it a practical alternative to smoothing/filtering and data assimilation on problems with state vectors of fairly large dimensions, as well as a large total number of time steps.

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Authors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA

    Francis J. Alexander

  2. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, 21218, USA

    Gregory L. Eyink

  3. Mathematics Department and Physics Department, University of Arizona, Tucson, AZ, 85721, USA

    Juan M. Restrepo

Authors
  1. Francis J. Alexander
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  2. Gregory L. Eyink
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  3. Juan M. Restrepo
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Correspondence to Francis J. Alexander.

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Alexander, F.J., Eyink, G.L. & Restrepo, J.M. Accelerated Monte Carlo for Optimal Estimation of Time Series. J Stat Phys 119, 1331–1345 (2005). https://doi.org/10.1007/s10955-005-3770-1

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  • DOI: https://doi.org/10.1007/s10955-005-3770-1

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