Statistics and Computing

, Volume 25, Issue 2, pp 427–437 | Cite as

Posterior inference on parameters of stochastic differential equations via non-linear Gaussian filtering and adaptive MCMC

  • Simo Särkkä
  • Jouni Hartikainen
  • Isambi Sailon Mbalawata
  • Heikki Haario


This article is concerned with Bayesian estimation of parameters in non-linear multivariate stochastic differential equation (SDE) models occurring, for example, in physics, engineering, and financial applications. In particular, we study the use of adaptive Markov chain Monte Carlo (AMCMC) based numerical integration methods with non-linear Kalman-type approximate Gaussian filters for parameter estimation in non-linear SDEs. We study the accuracy and computational efficiency of gradient-free sigma-point approximations (Gaussian quadratures) in the context of parameter estimation, and compare them with Taylor series and particle MCMC approximations. The results indicate that the sigma-point based Gaussian approximations lead to better approximations of the parameter posterior distribution than the Taylor series, and the accuracy of the approximations is comparable to that of the computationally significantly heavier particle MCMC approximations.


Stochastic differential equation Parameter estimation Gaussian approximation Non-linear Kalman filter Adaptive Markov chain Monte Carlo 



The authors would like to thank Marko Laine for his valuable help in AMCMC methods, and the anonymous referees for their suggestions for improving the paper.

Supplementary material (366 kb)
Supplementary Material for “Posterior Inference on Parameters of Stochastic Differential Equations via Non-Linear Gaussian Filtering and Adaptive MCMC” (PS 366 kB)


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Simo Särkkä
    • 1
  • Jouni Hartikainen
    • 1
  • Isambi Sailon Mbalawata
    • 1
  • Heikki Haario
    • 1
  1. 1.AaltoFinland

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