A Bayesian Nonparametric Approach to Dynamical Noise Reduction

TL;DR

This paper introduces a Bayesian nonparametric method using MCMC to reduce dynamical noise in chaotic time series, effectively reconstructing underlying dynamics even with heavy-tailed noise.

Contribution

It presents the DNRR model that simultaneously reconstructs dynamic equations and reduces noise, a novel approach for chaotic time series analysis.

Findings

Effective noise reduction demonstrated on synthetic data

Reconstruction of underlying dynamics achieved

Handles heavy-tailed noise distributions

Abstract

We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods (MCMC). The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator (DNRR) model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.