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Parameter estimation for random dynamical systems using slice sampling

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  • Hatjispyros, S.J.
  • Nicoleris, Theodoros
  • Walker, Stephen G.

Abstract

We provide details on the full reconstruction of the dynamic equations from measured time series data, given the general class of the underlying physical process. Our results can be used by researchers in physical modelling and statistical mechanics interested in an efficient estimation of low dimensional models, incorporating dynamic as well as observational noise. Our approach is Bayesian, based on an auxiliary variables algorithm that is fast and accurate, and direct, in the sense that only uniform distributions need to be sampled. This method is simpler than other Bayesian approaches where one has to sample from non-standard–unknown distributions using MCMC methods.

Suggested Citation

  • Hatjispyros, S.J. & Nicoleris, Theodoros & Walker, Stephen G., 2007. "Parameter estimation for random dynamical systems using slice sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 71-81.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:71-81
    DOI: 10.1016/j.physa.2007.03.013
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    References listed on IDEAS

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    1. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    2. Schenk-Hoppe, Klaus Reiner, 2005. "Poverty traps and business cycles in a stochastic overlapping generations economy with S-shaped law of motion," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 275-288, June.
    3. Hatjispyros, S.J. & Yannacopoulos, A.N., 2005. "A random dynamical system model of a stylized equity market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 583-612.
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    1. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    2. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2009. "A Bayesian nonparametric study of a dynamic nonlinear model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3948-3956, October.

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    Keywords

    Slice sampler; Random dynamical systems;

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