Joint reconstruction and prediction\break of random dynamical systems under\break borrowing of strength

We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo methods for the joint reconstruction and prediction of discrete time stochastic dynamical systems based on m-multiple time-series data, perturbed by additive dynamical noise. We introduce the Pairwise Dependent Geometric Stick-Breaking Reconstruction (PD-GSBR) model, which relies on the construction of an m-variate nonparametric prior over the space of densities supported over R^m. We are focusing on the case where at least one of the time-series has a sufficiently large sample size representation for an independent and accurate Geometric Stick-Breaking estimation, as defined in Merkatas et al. [Chaos 27, 063116 (2017)]. Our contention is that whenever the dynamical error processes perturbing the underlying dynamical systems share common characteristics, underrepresented data sets can benefit in terms of model estimation accuracy. The PD-GSBR estimation and prediction procedure is demonstrated specifically in the case of maps with polynomial nonlinearities of an arbitrary degree. Simulations based on synthetic time-series are presented.

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

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. 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 an 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.