Article

Journal of Signal Processing Systems

, Volume 61, Issue 1, pp 51-59

First online:

A Comparison of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems

  • Yuan ShenAffiliated withNeural Computing Research Group, Aston University Email author 
  • , Cedric ArchambeauAffiliated withDepartment of Computer Science, University College London
  • , Dan CornfordAffiliated withNeural Computing Research Group, Aston University
  • , Manfred OpperAffiliated withArtificial Intelligence Group, Technical University Berlin
  • , John Shawe-TaylorAffiliated withDepartment of Computer Science, University College London
  • , Remi BarillecAffiliated withNeural Computing Research Group, Aston University

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Abstract

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother.

Keywords

Data assimilation Signal processing Nonlinear smoothing Variational approximation Bayesian computation