Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Jaya Bishwal
University of North Carolina, Charlotte (SAMSI)
"Bernstein-von Mises Theorem for Stochastic Partial Differential Equations"
ABSTRACT
Stochastic partial differential equations (SPDEs) are continuous time spatio-temporal models driven by space-time white noise and have wide range of applications in finance, biology, oceanography and environmental science. For instance, in the theory of term structure of interest rates, the forward rate evolves as a parabolic SPDE. We study parameter estimation in such models through spectral approach and Bayesian method. First we discuss continuous time data and then we consider observations at discrete (possibly random, for instance, at the arrivals of a Poisson process) time points. We obtain the Bernstein-von Mises theorem concerning the convergence of suitably normalized and centered posterior distribution to normal distribution when the number of Fourier coefficients of the random filed increases. As a consequence we show the asymptotic equivalence of the maximum likelihood estimator and regular Bayes estimators and asymptotic efficiency of the Bayes estimators. We discuss extensions to partially observed (hidden) SPDE models, which for instance includes the stochastic volatility models, with the implementation of sequential monte carlo methods (particle filters).
Tuesday, October, 14, 2008
4:00 - 5:00 pm
208 Patterson Hall