BOCPD

BOCPD, Bayesian Online Change Point Detection, is a statistical framework for real-time identification of change points in sequential data. Introduced by Adams and MacKay in 2007, it provides probabilistic estimates of when the data-generating process changes and does so in an online, recursive fashion.

The core idea is to maintain a posterior distribution over the run length, defined as the number of observations since the last change point. At each new observation x_t, BOCPD updates the run-length distribution P(r_t | x_{1:t}) using the predictive distribution P(x_t | history within the current run) and a hazard function H(r) that encodes the prior probability of a change point after r observations. This produces a time-updated estimate of the probability that a change point occurred at time t and a distribution over possible run lengths. The method is online and produces immediate probabilistic assessments without requiring reprocessing of past data.

BOCPD requires an assumed data model: data within each segment are generated by a fixed set of parameters. The approach is agnostic about the specific likelihood model beyond having a tractable predictive distribution, often Gaussian for continuous data or categorical for discrete data, with conjugate priors to enable efficient updates. Extensions include alternative hazard functions, nonparametric likelihoods, and smoothing variants that combine online and retrospective inference.

Applications span finance for regime change detection, climate and environmental time series, neuroscience signals such as EEG, industrial process monitoring, and genomics. Advantages include probabilistic uncertainty quantification and real-time detection, while limitations involve sensitivity to the chosen hazard function and computational considerations for long run-length horizons.