Salon 2
Bayesian parameter inference for coupled SDEs using MCMC methods and density tracking by quadrature (303300)
Harish Bhat, University of California, MercedR. W. M. A Madushani, University of California, Merced
*Shagun Rawat, University of California, Merced
Keywords: Stochastic differential equations, Numerical simulation, Bayesian parameter inference, Monte Carlo algorithms
We consider a system that is modeled by coupled stochastic differential equations with unknown parameters. Given observations of the system in the form of vector-valued time series, our goal is to perform Bayesian inference of these parameters. A key challenge in developing a computationally efficient algorithm is the computation of the likelihood function on two-dimensional space. We address this issue by using a novel approach to track the intermediate transition densities by applying quadrature iteratively to the Euler-Maruyama approximation of the SDE. We reduce the computational time from O(n^4) to O(n^2) by integrating in the proximity of the Gaussian conditional density function. Computational results support our view that using the density tracking by quadrature (DTQ) method to compute the likelihood yields more accurate posteriors than using a purely Gaussian likelihood. Using the DTQ method, we compute both the likelihood and its gradient with respect to the parameters. In this way, we construct and compare Metropolis and Hamiltonian Monte Carlo methods for sampling from the posterior.