MCMC Algorithms for Bayesian Inference with Stochastic Differential Equations

• Activity Number: 427
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Harish S. Bhat* and R. W. M. A. Madushani and Shagun Rawat
• Companies: University of California at Merced and University of California at Merced and University of California at Merced
• Keywords: Bayesian ; stochastic differential equations ; inference ; Metropolis-Hastings ; MCMC ; time series

Abstract

We develop MCMC algorithms to perform Bayesian inference for models given by a class of stochastic differential equations. A key challenge in developing practical algorithms is the computation of the likelihood. We address this problem through the use of a fast, convergent method to track the probability density function of the stochastic differential equation. When the data consists of one or more time series, this method enables accurate, parallelizable computation of the likelihood. Computational tests show that the resulting Metropolis-Hastings algorithm is capable of efficient inference for several nonlinear models. The inference method adapts well to scenarios in which the data consists of many samples at one point in time, or when the data consists of one or more time series. After establishing the above results for scalar models, we extend the method to state-space models where the data consists of noisy and/or partial observations of the system's true state vector. We compare the results of our method against existing inference methods, highlighting the method's performance in terms of accuracy and speed as a function of the dimension of the state and parameter spaces.