Change Point Detection

A change point is a time at which the process generating a sequence changes in a meaningful way. The changed property may be a mean, variance, slope, distribution or relationship among variables. Detection matters in quality control, monitoring and time-series analysis because a single model fitted across different regimes can hide changes or produce misleading forecasts. Offline methods analyze a completed sequence and estimate where changes occurred. They often divide the data into segments and minimize a sum of within-segment costs plus a penalty for each change. The penalty controls complexity: too low can over-segment noise, while too high can miss real changes. PELT is an exact penalized segmentation algorithm for supported cost functions and pruning conditions, with favorable computational behavior in many settings; it is not a guarantee of the right penalty or a universal runtime bound. CUSUM is a sequential monitoring method that accumulates evidence of deviation from a reference. A threshold determines when to signal, with tradeoffs between detection delay and false alarms. Bayesian online methods maintain probabilities over run lengths, the time since the last change, and update those probabilities as observations arrive. These approaches differ in latency and whether they may revise a historical segmentation. A detected change is statistical evidence, not an explanation. It may reflect a real process intervention, seasonality, sensor drift, an outlier or a data-pipeline change. Evaluate sensitivity to minimum segment length, cost function and penalty, and account for autocorrelation and multiple monitoring opportunities. If a change point is found retrospectively after searching many locations, uncertainty in its position and false-discovery risk matter. For operational use, define what action follows an alert and track false alarms and missed changes. The algorithm can identify a boundary under its objective; domain investigation determines what happened and whether the system should respond.