rareevent

A rare event is a phenomenon with a very low probability of occurrence within a stochastic process. In statistics, rare events are infrequent outcomes that can have outsized effects when they occur, often appearing as extreme observations in large samples.

Rare events pose data- and modeling challenges because they are sparsely observed and the data are highly imbalanced. They may be clustered in time or space, and nonstationarity or regime changes can further complicate estimation.

Common approaches include probabilistic models for counts (Poisson, negative binomial) and their zero-inflated or hurdle variants for excess zeros. Extreme value theory focuses on tail behavior, while rare-event simulation and importance sampling aim to estimate very small probabilities.

Machine learning methods include anomaly detection and one-class classification, designed to identify rare patterns without requiring large samples of the rare class. Oversampling, undersampling, or synthetic data generation can help training, but risk overfitting.

Evaluation emphasizes recall and precision on the rare class. Metrics such as the F1 score and the area under the precision-recall curve (AUPRC) are often preferred to accuracy when dealing with imbalanced data.

Applications span finance (fraud, defaults), insurance claims, cybersecurity (intrusions, fraud), disaster risk and epidemiology, manufacturing (faults), and reliability engineering, where predicting or detecting rare events can prevent losses or save lives.

Data sources include historical records, sensor streams, and simulations. When using synthetic data, care must be taken to preserve temporal and spatial structure and to avoid bias. Ethical and regulatory considerations are also important in sensitive domains.