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

Isambi Mbalawata (), Simo Särkkä () and Heikki Haario ()

Computational Statistics, 2013, vol. 28, issue 3, 1195-1223

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

Keywords: Hamiltonian Monte Carlo; Stochastic differential equation; Parameter estimation; Markov chain Monte Carlo; Kalman filter; Matrix fraction decomposition (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:28:y:2013:i:3:p:1195-1223

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DOI: 10.1007/s00180-012-0352-y

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