Bayesian Nonparametric Reconstruction and Prediction of Nonlinear Dynamic Systems with Geometric Stick Breaking Noise
Spyridon J. Hatjispyros, Christos Merkatas · arXiv (Cornell University) · 2015
We propose a Bayesian nonparametric mixture model for the full dynamical equation reconstruction, from observed time series data, of discrete time one dimensional nonlinear random dynamical systems, based on the Geometric Stick Breaking process introduced by Fuentes-Garc\'ia et al. (2010). We provide a comparison study with models using Dirichlet process based mixtures. We demonstrate the inference procedure when the functional form of the deterministic part of the reconstruction equation is a polynomial and the nonparametric component is applied to additive errors. Our contention is that for dynamical reconstruction and prediction purposes, Geometric Stick Breaking process mixture priors are sufficient. Finally, we give evidence that it is possible to estimate the quasi-invariant measure of a noisy chaotic dynamical system using a relatively small data set. Simulations and a real US GNP data example are presented.