  System identification is of special interest in science and engineering. This
article is concerned with a system identification problem arising in stochastic
dynamic systems, where the aim is to estimating the parameters of a system
along with its unknown noise processes. In particular, we propose a Bayesian
nonparametric approach for system identification in discrete time nonlinear
random dynamical systems assuming only the order of the Markov process is
known. The proposed method replaces the assumption of Gaussian distributed
error components with a highly flexible family of probability density functions
based on Bayesian nonparametric priors. Additionally, the functional form of
the system is estimated by leveraging Bayesian neural networks which also leads
to flexible uncertainty quantification. Asymptotically on the number of hidden
neurons, the proposed model converges to full nonparametric Bayesian regression
model. A Gibbs sampler for posterior inference is proposed and its
effectiveness is illustrated in simulated and real time series.
