Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization

• Activity Number: 607
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Grant Schneider*+
• Keywords: SMLE ; SDE ; Pedersen

Abstract

Stochastic Differential Equations (SDEs) are used to model processes from many different disciplines, including finance, biology, and engineering. While these processes are continuously defined, inference is based on data observed at only a finite number of locations. This typically leads to intractable likelihoods, which causes difficulty in statistical inference, as it is impossible to observe a complete path in practice.

Sequential Monte Carlo is a popular method for estimating the likelihood of the data. Much of the previous work has focused on efficiently estimating the likelihood at fixed parameter values.

We propose an efficient Gaussian-process-based method for exploring the parameter space which accounts for the inherent Monte Carlo variability of the simulated likelihood method and does not require knowledge of the gradient of the log-likelihood. Our sequential method offers significant computational efficiency over a naive approach based on estimating the likelihood over a grid of possible parameter values.