A Bayesian Parameter Learning Procedure for Nonlinear Dynamical Systems via the Ensemble Kalman Filter

Dynamical systems are a natural and convenient way to model the evolution of processes observed in practice. When uncertainty is considered and incorporated, these system become known as stochastic dynamical systems. Based on observations made from stochastic dynamical systems, we consider the issue of parameter learning, and a related state estimation problem. We develop a Markov Chain Monte Carlo (MCMC) algorithm, which is an iterative method, for parameter inference. Within the parameter learning steps, the MCMC algorithm requires to perform state estimation for which the target distribution is constructed by using the Ensemble Kalman filter (EnKF). The methodology is illustrated using two examples of nonlinear stochastic dynamical systems.