Bayesian on-line anticipation of critical transitions

TL;DR

This paper introduces a Bayesian data-driven method using stochastic differential equations and MCMC for real-time anticipation of critical transitions in complex systems, accounting for noise and nonlinearities.

Contribution

It presents a novel Bayesian approach with credibility bands and a linear segment fit for online prediction of critical transitions, improving reliability and interpretability.

Findings

Robust anticipation of critical transitions despite high noise levels

Ability to estimate the transition time horizon based on current data

Handles nonlinear time dependencies in system parameters

Abstract

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise levels like they are present in many real world systems. Since the parameter estimation is done by a Markov Chain Monte Carlo approach we have access to credibility bands allowing for a better interpretation of the reliability of the results. By introducing a Bayesian linear segment fit it is possible to give an estimate for the time horizon in which the transition will probably occur based on the current state of information. This approach is also able to handle nonlinear time dependencies of the parameter controlling the transition. In general the method could be used as a tool for on-line analysis to detect changes in the resilience of the system and to provide information on the probability of the occurrence of a critical transition in future.