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Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering

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  • Isambi Mbalawata
  • Simo Särkkä
  • Heikki Haario

Abstract

This paper is concerned with parameter estimation in linear and non-linear Itô type stochastic differential equations using Markov chain Monte Carlo (MCMC) methods. The MCMC methods studied in this paper are the Metropolis–Hastings and Hamiltonian Monte Carlo (HMC) algorithms. In these kind of models, the computation of the energy function gradient needed by HMC and gradient based optimization methods is non-trivial, and here we show how the gradient can be computed with a linear or non-linear Kalman filter-like recursion. We shall also show how in the linear case the differential equations in the gradient recursion equations can be solved using the matrix fraction decomposition. Numerical results for simulated examples are presented and discussed in detail. Copyright Springer-Verlag 2013

Suggested Citation

  • Isambi Mbalawata & Simo Särkkä & Heikki Haario, 2013. "Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering," Computational Statistics, Springer, vol. 28(3), pages 1195-1223, June.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:3:p:1195-1223
    DOI: 10.1007/s00180-012-0352-y
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    2. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.
    3. Raillon, L. & Ghiaus, C., 2018. "An efficient Bayesian experimental calibration of dynamic thermal models," Energy, Elsevier, vol. 152(C), pages 818-833.
    4. Sy-Miin Chow & Lu Ou & Arridhana Ciptadi & Emily B. Prince & Dongjun You & Michael D. Hunter & James M. Rehg & Agata Rozga & Daniel S. Messinger, 2018. "Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 476-510, June.
    5. Ndanguza, Denis & Mbalawata, Isambi S. & Haario, Heikki & Tchuenche, Jean M., 2017. "Analysis of bias in an Ebola epidemic model by extended Kalman filter approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 113-129.

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