  We propose a Bayesian nonparametric mixture model for the reconstruction and
prediction from observed time series data, of discretized stochastic dynamical
systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be
used by researchers in physical modeling interested in a fast and accurate
estimation of low dimensional stochastic models when the size of the observed
time series is small and the noise process (perhaps) is non-Gaussian. The
inference procedure is demonstrated specifically in the case of polynomial maps
of arbitrary degree and when a Geometric Stick Breaking mixture process prior
over the space of densities, is applied to the additive errors. Our method is
parsimonious compared to Bayesian nonparametric techniques based on Dirichlet
process mixtures, flexible and general. Simulations based on synthetic time
series are presented.
