  We propose a Bayesian nonparametric approach for the noise reduction of a
given chaotic time series contaminated by dynamical noise, based on Markov
Chain Monte Carlo methods (MCMC). The underlying unknown noise process
(possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise
Reduction Replicator (DNRR) model with which we reconstruct the unknown dynamic
equations and in parallel we replicate the dynamics under reduced noise level
dynamical perturbations. The dynamic noise reduction procedure is demonstrated
specifically in the case of polynomial maps. Simulations based on synthetic
time series are presented.
