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

Abstract

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 Rm. 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.