Exact Sampling and Inference for Non-Linear Stochastic Differential Equations. Short course By Prof. Alexandros Beskos (Associate Professor at NUS, Singapore)
Exact Sampling and Inference for Non-Linear Stochastic Differential Equations. I will present a surprisingly simple algorithm we developed some years ago for the exact simulation of non-linear diffusion processes. Exact sampling of such processes was considered impossible for such models. The presence of stochasticity allows for developing a rejection sampling algorithm by proposing candidate Brownian paths; the accept/reject rule then involves events of an appropriate Poisson process. We have thus termed the method the Weiner-Poisson factorization of a non-linear SDE. The developed sampling method provides also a natural approach for carrying out maximum-likelihood-based inference for unknown parameters of the SDE.
Overview
Abstract
Exact Sampling and Inference for Non-Linear Stochastic Differential Equations.
I will present a surprisingly simple algorithm we developed some years ago for the exact simulation of non-linear diffusion processes. Exact sampling of such processes was considered impossible for such models. The presence of stochasticity allows for developing a rejection sampling algorithm by proposing candidate Brownian paths; the accept/reject rule then involves events of an appropriate Poisson process. We have thus termed the method the Weiner-Poisson factorization of a non-linear SDE. The developed sampling method provides also a natural approach for carrying out maximum-likelihood-based inference for unknown parameters of the SDE.
We show a number of extensions we obtained on the initial algorithm, corresponding to fewer restrictions on the drift function. I will discuss some open problems, limitations of the methods, and recent advances. Our work was published as a discussion paper at JRSSB in 2006, with several later extensions.
Brief Biography
2013-Today: Senior Lecturer in Statistics at UCL and Associate Professor at NUS.
2008-2013: Lecturer in Statistics at UCL.
2005-2008: Post-Doc in Mathematics Institute and Department of Statistics, at University of Warwick.
2002-2005: PhD under the supervision of Professor Gareth Roberts
Refreshments: Available @ 2:45pm on Thursday
