Early Warning Signals and the Prosecutor's Fallacy

Abstract

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on temporal and spatial scales that can be difficult to approach by experimental manipulation, research has often relied on historical observations as a source of natural experiments. Here we examine a critical difference between selecting systems for study based on the fact that we have observed a critical transition and those systems for which we wish to forecast the approach of a transition. This difference arises by conditionally selecting systems known to experience a transition of some sort and failing to account for the bias this introduces -- a statistical error often known as the Prosecutor's Fallacy. By analysing simulated systems that have experienced transitions purely by chance, we reveal an elevated rate of false positives in common warning signal statistics. We further demonstrate a model-based approach that is less subject to this bias than these more commonly used summary statistics. We note that experimental studies with replicates avoid this pitfall entirely.

3 figures; Proceedings of the Royal Society B 2012

References in corpus (1)

• Climate tipping as a noisy bifurcation: a predictive technique

Cited by in corpus (13)

• Structure and dynamics of molecular networks: A novel paradigm of drug discovery. A comprehensive review
• Early warning signals: The charted and uncharted territories
• No evidence for critical slowing down prior to human epileptic seizures
• Dynamics of a producer-parasite ecosystem on the brink of collapse
• Probability of noise- and rate-induced tipping
• No early warning signals for stochastic transitions: insights from large deviation theory
• Stochastic Desertification
• Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems
• Quantifying resilience and the risk of regime shifts under strong correlated noise
• Buffering variability in cell regulation motifs close to criticality
• Early Warning Signals for Bifurcations Embedded in High Dimensions
• Bayesian on-line anticipation of critical transitions
• Interpretable Early Warnings using Machine Learning in an Online Game-experiment