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Activity Number: 467
Type: Invited
Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #314166 View Presentation
Title: Bridge Simulation and Estimation for Multivariate Stochastic Differential Equations
Author(s): Michael Sørensen*
Companies: University of Copenhagen
Keywords: discretely sampled diffusions ; stochastic differential equation ; Bayesian inference ; likelihood inference ; coupling ; time-reversal
Abstract:

New simple methods of simulating multivariate diffusion bridges are presented. Diffusion bridge simulation plays a fundamental role in simulation-based likelihood inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes the one-dimensional bridge-simulation method proposed by Bladt and Sørensen (2014) to the multivariate setting. A method of simulating approximate, but often very accurate, diffusion bridges is proposed. These approximate bridges are used as proposal for easily implementable MCMC algorithms that produce exact diffusion bridges. The new method is more generally applicable than previous methods because it does not require the existence of a Lamperti transformation, which rarely exists for multivariate diffusions. Another advantage is that the new method works well for diffusion bridges in long intervals because the computational complexity of the method is linear in the length of the interval. The usefulness of the new method is illustrated by an application to Bayesian estimation for the multivariate hyperbolic diffusion model. Based on joint work by M. Bladt, S. Finch and M. Sørensen.


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