Bayesian reconstruction of chaotic dynamical systems

We present a Bayesian approach to the problem of determining parameters of nonlinear models from time series of noisy data. Recent approaches to this problem have been statistically flawed. By applying a Markov chain Monte Carlo algorithm, specifically the Gibbs sampler, we estimate the parameters of chaotic maps. A complete statistical analysis is presented, the Gibbs sampler method is described in detail, and example applications are presented.