A Bayesian Nonparametric approach to Reconstruction and Prediction of Random Dynamical Systems

TL;DR

This paper introduces a Bayesian nonparametric mixture model using MCMC for reconstructing and predicting stochastic dynamical systems from limited time series data, accommodating non-Gaussian noise and polynomial maps.

Contribution

It presents a novel, flexible Bayesian nonparametric approach with a Geometric Stick Breaking prior for modeling stochastic dynamical systems, improving estimation with small data sets.

Findings

Effective reconstruction of stochastic systems demonstrated on synthetic data

Handles non-Gaussian noise in dynamical systems

More parsimonious than Dirichlet process mixture models

Abstract

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 (MCMC). 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 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.