A Gibbs Sampler for Bayesian Nonparametric State-Space Models

A common assumption in state space models is that the state and observation noise is Gaussian. However, there are cases where this assumption is violated and is chosen for computational convenience. In this article, we present a state space model whose noise processes are modeled via highly flexible density functions based on Bayesian nonparametric priors with decreasing weights. We are focusing on a system identification problem were the aim is to estimate the parameters and the states of the (possibly) nonlinear dynamical system along with its noise processes using Gibbs sampling. Experiments in simulated data show that the nonparametric model outperforms parametric models especially when the distributions of the noise processes depart from Gaussianity.