Change Point Detection

Change point detection involves identifying points in time where the statistical properties of a time series change significantly. This can be formalized through various statistical tests, such as the CUSUM (Cumulative Sum Control Chart) or Bayesian change point analysis. Mathematically, a change point is defined as a point in the time series where the probability distribution of the data shifts, indicating a regime change. Algorithms for change point detection often utilize likelihood ratios or Bayesian inference to determine the most probable change points. This technique is essential for monitoring systems and detecting anomalies, as it allows for timely interventions in dynamic environments.