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Posterior Inference on Parameters of Stochastic Differential Equations via Gaussian Process Approximations
This talk is concerned with Bayesian estimation of parameters in stochastic differential equation (SDE) models occurring in physics, engineering and financial applications. In particular, the talk is considered with implementation of MCMC based sampling methods for partially observed irreducible Brownian-motion-driven non-linear multivariate SDEs. For these kind of SDEs computation of the transition densities is not possible in closed form and thus the implementation of MCMC methods is not possible without additional approximations. In this talk we show how Taylor series and Gaussian cubature methods can be used for forming Gaussian approximations to the transition densities and how non-linear Kalman filters can be used in efficient implementation of MCMC sampling. In addition to MCMC, we also discuss implementation of Laplace approximations and other types of methods for the posterior parameter inference by using similar approximations.
Dr. Simo Särkkä is Senior Researcher with the Department of Biomedical Engineering and Computational Science of Aalto University, Finland. He is also a Docent (~Adjunct Professor) with the Tampere University of Technology (TUT), Tampere, Finland and with the Lappeenranta University of Technology (LUT), Lappeenranta, Finland. During the year 2011 he was a visiting scholar with the Signal Processing and Communications Laboratory, Department of Engineering, University of Cambridge, UK. His research interests are in Bayesian estimation of stochastic dynamic systems, spatio-temporal systems and their applications in brain imaging, positioning systems and signal processing. He has authored or co-authored over 30 articles on the abovementioned subjects.