BOCPD key terms

An online algorithm that maintains a probability distribution over how long the current run of data has lasted, updating it recursively as each new observation arrives so changepoints are flagged without reprocessing history.

A time index where the statistical behavior of a data stream shifts, such as a change in mean, variance, or trend. Detection aims to locate such indices as quickly and reliably as possible.

The number of observations since the most recent changepoint. In BOCPD it is a latent variable, and the algorithm tracks a probability for each possible run length value.

A normalized distribution over all candidate run lengths after observing data up to the current time. It concentrates mass near zero when a changepoint is likely.

The recursive step that combines the previous run length distribution, the hazard rate, and the predictive likelihood of the new datum to produce the current run length distribution.

The probability assigned to the next observation given the data seen so far within a run. It is computed from the conjugate posterior of the underlying data model.

The prior probability that a changepoint occurs at each time step, independent of the data. A constant hazard yields a geometric prior over run lengths.

A distribution over run lengths implied by a constant hazard rate, where the chance of continuing a run decays by the same factor at every step.

The posterior mass placed on run length zero at a given time step, interpreted as the estimated probability that a change just occurred at that observation.

A prior distribution that, combined with a given likelihood, yields a posterior of the same family. This keeps BOCPD updates closed-form and cheap to compute.

Compact summaries of the data within a run, such as counts, sums, and sums of squares, that are all that is needed to update the predictive distribution.

A conjugate prior for a Gaussian model with unknown mean and variance, parameterized by prior mean, scale, and shape values that are updated with each observation.

An assumption that observations within a run follow a normal distribution. It underlies many BOCPD implementations and yields Student-t predictive distributions.

Choosing the data model, prior, and hazard settings that best match the application. Poor choices cause missed changes or excessive false alarms.

Setting initial hyperparameters, such as the expected run length or prior scale, before streaming data. These choices shape early behavior and sensitivity.

The mean number of observations between changepoints implied by the hazard setting. It is roughly the reciprocal of a constant hazard rate.

The computational pattern in which the run length distribution at one step is computed solely from the previous step's distribution and the new datum, avoiding storage of full history.

The cost of a BOCPD update. Naive updates grow linearly with the number of candidate run lengths, giving quadratic total cost over a stream unless pruning is applied.

Discarding candidate run lengths whose posterior probability falls below a small threshold, which bounds memory and computation while barely affecting accuracy.

Techniques that trade exactness for speed, such as capping the maximum run length, merging low-probability states, or subsampling, used when exact BOCPD is too costly.

A cap on the largest run length tracked, which limits memory growth. It slightly biases detection for very long stable periods but keeps updates bounded.

Declaring a changepoint when the changepoint probability or a related statistic crosses a chosen level. The threshold controls the trade-off between sensitivity and false alarms.

A declared changepoint when none actually occurred. Frequent false alarms erode trust and trigger unnecessary downstream actions.

The number of observations between a true changepoint and its detection. Lower delay means faster response but usually more false alarms.

The expected frequency of spurious detections over a period, often expressed per observation or per unit time. It is tuned through hazard and threshold settings.

Balancing detection delay against false alarm rate when tuning a detector. Curves plotting one against the other help compare configurations objectively.

Analysis performed on a complete dataset, where the number and locations of changes are estimated jointly. It contrasts with online detection, which must decide in real time.

Sequential analysis that processes each observation once, as it arrives, and must issue decisions without knowledge of future data.

Reviewing a stream after the fact to confirm, relabel, or explain detections. It is often used to validate an online detector's output.

The known or annotated changepoint locations used to evaluate a detector, typically in simulation studies or labeled historical data.

Evaluation metrics for detection: precision is the share of declared changepoints that are real, and recall is the share of real changepoints that were found.

Gradual or abrupt change in the data-generating process over time. BOCPD addresses abrupt drift but may need extensions for slow, incremental shifts.

Identifying unusual observations or periods. Changepoint methods complement anomaly detection by flagging shifts in normal behavior rather than single outliers.

A potentially unbounded sequence of observations arriving over time, which motivates the incremental, memory-bounded design of online changepoint algorithms.

Adjusting settings such as hazard rate, prior scale, and detection threshold using validation data or simulation to meet accuracy and latency goals.

A contiguous block of observations between two changepoints that is treated as sharing one statistical regime for modeling purposes.

Comparing simulated data from the fitted model with observed data to judge whether the model and priors are reasonable for the stream.