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We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo(MCMC) methods for the joint reconstruction and prediction of discrete timestochastic dynamical systems, based on $m$-multiple time-series data, perturbedby additive dynamical noise. We introduce the Pairwise Dependent GeometricStick-Breaking Reconstruction (PD-GSBR) model, which relies on the constructionof a $m$-variate nonparametric prior over the space of densities supported over$\mathbb{R}^m$. We are focusing in the case where at least one of thetime-series has a sufficiently large sample size representation for anindependent and accurate Geometric Stick-Breaking estimation, as defined inMerkatas et al. (2017). Our contention, is that whenever the dynamical errorprocesses perturbing the underlying dynamical systems share commoncharacteristics, underrepresented data sets can benefit in terms of modelestimation accuracy. The PD-GSBR estimation and prediction procedure isdemonstrated specifically in the case of maps with polynomial nonlinearities ofan arbitrary degree. Simulations based on synthetic time-series are presented.

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