Bayesian on-line anticipation of critical transitions

The design of reliable indicators to anticipate critical transitions in complex systems is an important task in order to detect imminent regime shifts and to intervene at an early stage to either prevent them or mitigate their 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 which is a characteristic of 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. We also show that the method can yield meaningful results under correlated noise. 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 that controls the transition. The method can 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 critical transitions in future. Additionally, it can give valuable information about the possibility of noise induced transitions. The discussed methods are made easily accessible via a flexibly adaptable open source toolkit named 'antiCPy' which is implemented in the programming language Python.