ChangePointDetection

ChangePointDetection refers to the statistical task of identifying times when the probabilistic properties of a sequence of observations change. A change point marks a boundary between segments that are governed by different data-generating processes, such as shifts in the mean, variance, or distribution. The problem is common in time series analysis, signal processing, genomics, and finance, where timely detection is important for interpretation and action.

Approaches are generally classified as offline (retrospective) or online (real-time). Offline methods evaluate the entire sequence to locate all change points, while online methods emit detections as new data arrive. Many methods assume a parametric model for the data, but nonparametric techniques are also used when distributional form is uncertain.

Prominent techniques include CUSUM and other sequential likelihood ratio tests for detecting shifts in mean; penalized likelihood methods such as the Pruned Exact Linear Time (PELT) algorithm; and binary segmentation. Bayesian methods, including Bayesian Online Change Point Detection, maintain posterior beliefs about run length and detect changes based on posterior probabilities. Hybrid and multivariate methods extend to more than one time series or to changes in variance and correlations.

Applications span finance for regime shifts, climate science for abrupt changes in weather patterns, genomics for copy number variation, network monitoring for traffic anomalies, and quality control in manufacturing. Practical challenges include choosing the number of changes, handling gradual or multiple severities, and robustness to noise and model misspecification.

Evaluation often uses simulated data with known change points or cross-validation on historical records, and performance is summarized with detection delay, false alarm rate, and accuracy of estimated change points.