System identification using Bayesian neural networks with nonparametric noise models

System identification is of special interest in science and engineering. This\narticle is concerned with a system identification problem arising in stochastic\ndynamic systems, where the aim is to estimate the parameters of a system along\nwith its unknown noise processes. In particular, we propose a Bayesian\nnonparametric approach for system identification in discrete time nonlinear\nrandom dynamical systems assuming only the order of the Markov process is\nknown. The proposed method replaces the assumption of Gaussian distributed\nerror components with a highly flexible family of probability density functions\nbased on Bayesian nonparametric priors. Additionally, the functional form of\nthe system is estimated by leveraging Bayesian neural networks which also leads\nto flexible uncertainty quantification. Asymptotically on the number of hidden\nneurons, the proposed model converges to full nonparametric Bayesian regression\nmodel. A Gibbs sampler for posterior inference is proposed and its\neffectiveness is illustrated on simulated and real time series.\n