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

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Abstract

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.

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Acknowledgements

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.

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  1. P.O. Box 12200, 00076, Aalto, Finland

    Simo Särkkä, Jouni Hartikainen, Isambi Sailon Mbalawata & Heikki Haario

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  1. Simo Särkkä
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  2. Jouni Hartikainen
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  3. Isambi Sailon Mbalawata
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Correspondence to Simo Särkkä.

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Särkkä, S., Hartikainen, J., Mbalawata, I.S. et al. Posterior inference on parameters of stochastic differential equations via non-linear Gaussian filtering and adaptive MCMC. Stat Comput 25, 427–437 (2015). https://doi.org/10.1007/s11222-013-9441-1

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