Probabilistic Early Warning Signals – Ville Laitinen

Probabilistic Early Warning Signals

Ville Laitinen, Department of Computing

Complex systems can exhibit multiple stable states separated by critical thresholds, and abrupt transitions between the alternative equilibria can occur with little change in the system’s state before the transition. There are numerous examples of such transitions in real-life systems, ranging from molecular mechanisms to ecosystems, including the human microbiome. Such transitions can have significant consequences, making accurate and reliable prediction essential for systems management.

Early warning signals (EWS) are statistical indicators that track a system’s dynamics and aim to indicate increased risk for a transition. Examples include a rise in autocorrelation and variance. Robust detection of EWS with current methodology relies on densely sampled longitudinal data, which can be difficult to acquire. However, methodological advances could potentially aid in dealing with limited data more effectively.

In this work, we show how Bayesian stochastic processes can be used to detect EWS in time series and reach higher sensitivity than the previously available methods. We formulate probabilistic variants of previously proposed time-varying processes and show how assumptions about the dynamics can be incorporated in the prior distributions. Moreover, we explore performance in data sets corrupted with observation error and show how the probabilistic framework enables robust uncertainty quantification. Simulations and real experimental data sets are used to demonstrate the performance of probabilistic early warning indicators.