An efficient Monte-Carlo algorithm for the ML-Type II parameter estimation of nonlinear diffusions

The mathematical framework of non-linear diffusions has been playing an important role in modelling natural phenomena. Recently, much efforts have been made in developing inferential methods for such stochastic dynamical systems. Both state- and parameter estimation are of interests. The state-of-art Hybrid-Monte Carlo method has been applied to state estimation of non-linear diffusions. For parameter estimation, the data augmentation strategy is often adopted. Accordingly, state and parameters are sampled in a Gibbs-sampler setting. However, it has been reported that such a Monte-Carlo algorithm has very poor mixing property. This is due to strong correlations between state and parameter samples. In this paper, we propose a maximal likelihood (ML) type II approach to parameter estimation. Equipped with the Wang-Landau algorithm from statistical physics, the novel algorithm is shown to be both accurate and efficient.