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AMS Seminar: Simulation And Estimation For Stochastic Differential Equations

Speaker Name: 
Harish Bhat
Speaker Title: 
Associate Professor
Speaker Organization: 
UC Merced
Start Time: 
Monday, November 6, 2017 - 4:00pm
End Time: 
Monday, November 6, 2017 - 5:00pm
Location: 
E2-180

Abstract

We consider the problem of estimating parameters in stochastic differential equation (SDE) models from discrete-time observations (time series). A key bottleneck is computation of the log likelihood. We describe a method, density tracking by quadrature (DTQ), to compute densities and likelihoods. DTQ consists of using quadrature to solve, at each time step, the Chapman-Kolmogorov equation associated with a time-discretization of the SDE. After motivating DTQ, we will discuss theoretical and empirical convergence results. These results include convergence in L^1 to both the exact pdf of the Markov chain (with exponential convergence rate), and to the exact pdf of the SDE (with linear convergence rate). We will show how to apply DTQ to estimation and inference problems in both Bayesian and nonparametric contexts, and describe future extensions to SDE driven by Levy noise.
 

Bio

Harish S. Bhat received the A.B. in Mathematics from Harvard in 2000 and the Ph.D. in Control and Dynamical Systems from Caltech in 2005.  He joined the UC Merced faculty in 2008 and is currently an Associate Professor in the Applied Mathematics Unit.  Since 2016, he has also served as the Chair of the Applied Mathematics Graduate Program.  Prior to UC Merced, he held a postdoctoral appointment at Columbia University and spent one year on the faculty of Claremont McKenna College.  His research interests include computational mathematics/statistics, stochastic processes, and machine learning.