An Imbalance-Robust Evaluation Framework for Extreme Risk Forecasts

Abstract: Evaluating rare-event forecasts is challenging because standard metrics collapse as event prevalence declines. Measures such as F1-score, AUPRC, MCC, and accuracy induce degenerate thresholds -- converging to zero or one -- and their values become dominated by class imbalance rather than tail discrimination. We develop a family of rare-event-stable (RES) metrics whose optimal thresholds remain strictly interior as the event probability approaches zero, ensuring coherent decision rules under extreme rarity. Simulations spanning event probabilities from 0.01 down to one in a million show that RES metrics maintain stable thresholds, consistent model rankings, and near-complete prevalence invariance, whereas traditional metrics exhibit statistically significant threshold drift and structural collapse. A credit-default application confirms these results: RES metrics yield interpretable probability-of-default cutoffs (4-9%) and remain robust under subsampling, while classical metrics fail operationally. The RES framework provides a principled, prevalence-invariant basis for evaluating extreme-risk forecasts.