{ "id": "ephjcp28c8", "slug": "change-point-detection", "title": "Change-point detection", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math" }, { "id": "physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics" }, { "id": "physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference" }, { "id": "physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Hypothesis testing", "api_url": 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"https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference.hypothesis_testing" } ] }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Non-geographic · 1946 to 2000: Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math" }, { "id": "geo.nongeo.t1946.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing" } ] } ], "excerpt": "Change-point detection comprises statistical methods for identifying when the distribution of a data series changes, using online procedures that alarm quickly or offline procedures that segment the series.", "snippet": "Change-point detection comprises statistical methods for identifying when the distribution of a data series changes, using online procedures that alarm quickly or offline procedures that segment the series.", "node": "physical.math.statistics.stats_statistical_inference.sequential_multiplicity.sequential_tests_general", "markdown": "# Change-point detection\n\nChange-point detection comprises statistical methods for identifying the times at which the distribution or the parameters of a data series change. Methods divide into online procedures, which process each observation as it arrives to raise an alarm quickly, and offline procedures, which retrospectively segment a complete series into stationary pieces.[1](https://ar5iv.labs.arxiv.org/html/1801.00718) The changes targeted include shifts in mean, changes in variance, and arbitrary distributional changes. The output depends on the method: classical sequential detectors return a single alarm time, offline penalized optimization returns a segmentation, and Bayesian online methods return a full posterior distribution over the run length, the time since the last change.[2](https://doi.org/10.48550/arxiv.0710.3742) Offline segmentation is typically solved by dynamic programming or greedily; online detection relies on CUSUM-type statistics or Bayesian filtering.[3](http://temporalbook.apartsin.com/part-2-classical-forecasting/module-08-anomaly-changepoint/section-8.3.html)\n\n| Key fact | Detail |\n|---|---|\n| Two branches | Online detection alarms as data arrive; offline detection retrospectively segments the whole series[1](https://ar5iv.labs.arxiv.org/html/1801.00718) |\n| CUSUM | Proposed by E. S. Page in 1954, based on the log-likelihood ratio between known pre- and post-change distributions[4](https://doi.org/10.1093/biomet/41.1-2.100) |\n| Bayesian online output | A recursive message-passing algorithm yields the full posterior over the current run length[2](https://doi.org/10.48550/arxiv.0710.3742) |\n| Algorithm costs | Binary Segmentation is approximate at \\( O(T \\log T) \\); dynamic programming is exact but \\( O(T^{2}) \\); PELT is exact with expected \\( O(n) \\) cost[5](https://arxiv.org/pdf/1101.1438v3) • [6](https://doi.org/10.1214/14-aos1245) |\n| Delay bound | Expected detection delay scales as \\( \\log \\gamma \\) divided by the KL divergence between pre- and post-change densities[7](https://par.nsf.gov/servlets/purl/10492374) |\n| Penalties | AIC uses \\( \\beta = 2p \\) per change; BIC/SIC uses \\( \\beta = p \\log n \\), where p is the number of added parameters[5](https://arxiv.org/pdf/1101.1438v3) • [3](http://temporalbook.apartsin.com/part-2-classical-forecasting/module-08-anomaly-changepoint/section-8.3.html) |\n\n## How it works\n\nThe cumulative sum (CUSUM) detector accumulates the log-likelihood ratio of a post-change distribution against a pre-change distribution for each new sample and resets the accumulation whenever it would go negative; it alarms when the statistic crosses a threshold h, with a reference value k usually set to half the smallest shift worth detecting.[3](http://temporalbook.apartsin.com/part-2-classical-forecasting/module-08-anomaly-changepoint/section-8.3.html) For a single change at location \\( \\tau \\) in Gaussian data with known variance \\( \\sigma^{2} \\), the likelihood-ratio deviance, twice the log likelihood ratio, equals the squared CUSUM statistic rescaled by the variance, \\( 2\\log\\Lambda_{\\tau} = C_{\\tau}^{2}/\\sigma^{2} \\), which under no change follows a chi-squared distribution with one degree of freedom; with unknown location the test uses the maximum of \\( 2\\log\\Lambda_{\\tau} \\) over \\( \\tau \\), equivalent to the maximum squared CUSUM statistic.[8](https://ar5iv.labs.arxiv.org/html/2210.07066) The CUSUM statistic systematically compares the means of the data to the left and right of each candidate change-point.[9](https://www.lancaster.ac.uk/~romano/teaching/2425MATH337/MATH337--Changepoint-Detection.pdf)\n\nLorden (1971) established that the optimal expected detection delay among procedures with average run length at least γ is of order \\( \\log \\gamma \\) divided by the [Kullback–Leibler divergence](https://www.edgepedia.org/kullback-leibler-divergence) between pre- and post-change distributions, and Moustakides (1986) and Ritov (1990) showed that CUSUM is optimal in Lorden's worst-case framework.[10](https://wrap.warwick.ac.uk/id/eprint/189987/1/A%20note%20on%20online%20change%20point%20detection.pdf) The classical bound reads \\( \\mathrm{EDD} = \\log \\gamma (1+o(1))/D(f_{1}\\|f_{0}) \\) as \\( \\gamma \\to \\infty \\).[7](https://par.nsf.gov/servlets/purl/10492374) Offline, the standard objective minimizes the sum of segment costs plus a penalty per change-point; too small a penalty detects noise-induced changes, while too large a penalty detects only the most significant changes or none.[1](https://ar5iv.labs.arxiv.org/html/1801.00718)\n\n## How it is done\n\n**Offline search.** Binary Segmentation tests for a split at the cost-minimizing point and recurses; it is approximate and typically costs \\( O(T\\log T) \\).[6](https://doi.org/10.1214/14-aos1245) Optimal Partitioning, the dynamic programming algorithm of Jackson and colleagues (2005), is exact but quadratic in the data length.[11](https://doi.org/10.1109/lsp.2001.838216) PELT (Pruned Exact Linear Time), introduced by Killick, Fearnhead and Eckley (2012),[12](https://doi.org/10.1080/01621459.2012.737745) adds a pruning step to Optimal Partitioning that removes candidates that can never be optimal without affecting exactness; its worst-case cost is \\( O(n^{2}) \\), with expected cost \\( O(n) \\) when the number of change-points grows linearly with n.[5](https://arxiv.org/pdf/1101.1438v3) • [13](https://wrap.warwick.ac.uk/id/eprint/135155/7/WRAP-Univariate-mean-change-point-Yu-2020.pdf) FPOP and SNIP extend pruning further; FPOP always prunes more than PELT and is substantially faster than existing dynamic programming methods.[14](https://doi.org/10.1007/s11222-016-9636-3) The changepoint R package implements PELT and several search methods.[15](https://doi.org/10.18637/jss.v058.i03)\n\nPenalty choice controls the number of detected changes. AIC is well known to overestimate the true number of change-points, while BIC performs well among location-independent penalties.[16](https://digitalcommons.unl.edu/cgi/viewcontent.cgi?params=/context/statisticsfacpub/article/1167/&path_info=Lund_JC_2023_Good_Practices_and_Common_Pitfalls.pdf) Modified variants (mAIC, mBIC, MDL) exist; AIC and MDL tend to overestimate, and the mBIC2 penalty of \\( 3\\log N \\) tends to underestimate.[17](https://www.mdpi.com/1099-4300/26/1/50)\n\n**Online detection.** Sequential detectors are judged by the average run length (ARL), the expected stopping time under the pre-change distribution, and the expected detection delay (EDD); reducing the delay necessarily raises the false-alarm probability.[7](https://par.nsf.gov/servlets/purl/10492374) • [3](http://temporalbook.apartsin.com/part-2-classical-forecasting/module-08-anomaly-changepoint/section-8.3.html) Window-limited generalized likelihood ratio (GLR) detectors use memory \\( O(w) \\) and at least \\( O(w^{2}) \\) computation per time unit, reduced to \\( O(w) \\) for exponential families, and remain asymptotically optimal if \\( w \\geq \\log \\gamma / D_{\\min} \\).[7](https://par.nsf.gov/servlets/purl/10492374) FOCuS runs moving-window tests for all window sizes simultaneously via functional pruning, with expected per-iteration cost logarithmic in the number of observations.[18](https://www.jmlr.org/papers/volume24/21-1230/21-1230.pdf) Recent work extends exact online likelihood ratio computation to multivariate streams via computational geometry, with exact algorithms impractical when the dimension p exceeds 5.[19](https://academic.oup.com/jrsssb/article/88/1/171/8223216) Bayesian online changepoint detection computes the run-length posterior by message passing; the conditional prior puts mass only on the run continuing (\\( r_{t} = r_{t-1}+1 \\)) or resetting to zero, and with pruning of tail run-length mass the average per-step cost is on the order of the expected run length.[2](https://doi.org/10.48550/arxiv.0710.3742) Test power is linear in the number of points but quadratic in the change size, so roughly four times as much data is needed to detect a change half as big.[8](https://ar5iv.labs.arxiv.org/html/2210.07066)\n\n## Origin\n\nSequential monitoring began with the control chart of W. A. Shewhart (1925), which computes a statistic from every sample to maintain manufacturing quality.[20](https://doi.org/10.1080/01621459.1925.10502930) [Abraham Wald](https://www.edgepedia.org/abraham-wald)'s work on sequential analysis (1946) started the statistical study of online detection,[21](https://doi.org/10.1214/aoms/1177730889) and E. S. Page proposed the CUSUM procedure in 1954[4](https://doi.org/10.1093/biomet/41.1-2.100) and a test for a change in a parameter at an unknown point in 1955.[22](https://doi.org/10.1093/biomet/42.3-4.523) A. F. M. Smith (1975) reported a Bayesian approach to inference about a change-point in a sequence of random variables.[23](https://doi.org/10.1093/biomet/62.2.407) Bayesian online changepoint detection was reported by Ryan Prescott Adams and [David J. C. MacKay](https://www.edgepedia.org/david-j-c-mackay) in 2007.[2](https://doi.org/10.48550/arxiv.0710.3742)\n\n## Variants\n\n**Segmentation methods.** Wild Binary Segmentation (WBS) draws random subsamples, computes the CUSUM statistic on each, and takes the largest maximizer as the first change-point candidate, tested against a threshold and applied recursively; it remains consistent for very short spacings and small jumps, where standard Binary Segmentation is consistent only when the minimum spacing between adjacent change-points exceeds \\( T^{3/4} \\).[6](https://doi.org/10.1214/14-aos1245) WBS2 adaptively draws a small number of subsamples (about 100 in its numerical sections) and produces a complete solution path.[24](https://stats.lse.ac.uk/fryzlewicz/wbs2/wbs2sdll.pdf) Circular Binary Segmentation, reported by A. B. Olshen and colleagues in 2004, targets array-based DNA copy number data,[25](https://doi.org/10.1093/biostatistics/kxh008) and the Narrowest-over-Threshold method is a further improvement on Binary Segmentation.[26](https://www.annualreviews.org/content/journals/10.1146/annurev-statistics-041124-044143)\n\n**Kernel, Bayesian, and distribution-free methods.** Kernel Change-point Analysis (KCpA) uses a test statistic based on the maximum kernel Fisher discriminant ratio, with a derived limiting null distribution for principled thresholds.[27](https://proceedings.neurips.cc/paper_files/paper/2008/file/08b255a5d42b89b0585260b6f2360bdd-Paper.pdf) The online kernel change detection algorithm (KCD) of F. Desobry, M. Davy and C. Doncarli (2005) runs two [one-class support vector machines](https://www.edgepedia.org/one-class-support-vector-machine) on the left and right parts of a window.[28](https://doi.org/10.1109/tsp.2005.851098) • [27](https://proceedings.neurips.cc/paper_files/paper/2008/file/08b255a5d42b89b0585260b6f2360bdd-Paper.pdf) Robust Bayesian descendants include β-BOCD, based on generalised [Bayesian inference](https://www.edgepedia.org/bayesian-inference) with β-divergences, and Dm-BOCD, reported by Matias Altamirano, François-Xavier Briol and Jeremias Knoblauch (2023), which uses diffusion score matching, costs \\( O(T(d^{2}+p^{2})) \\) with Adams and MacKay's pruning, and was more than 10 times faster than β-BOCD in experiments.[29](https://proceedings.mlr.press/v202/altamirano23a/altamirano23a.pdf) The MOSUM procedure of Birte Eichinger and Claudia Kirch (2017) estimates multiple change-points via moving sums,[30](https://doi.org/10.3150/16-bej887) with an R package implementation,[31](https://doi.org/10.18637/jss.v097.i08) and the ID method of Andreas Anastasiou and Piotr Fryzlewicz (2021) isolates single generalized change-points.[32](https://doi.org/10.1007/s00184-021-00821-6) ART transforms observations into scores via a symmetric function so that under the null the scores are exchangeable, giving distribution-free, finite-sample Type I error control.[33](https://academic.oup.com/jrsssb/article/88/4/1278/8456337) In the Bayesian setting with a geometric prior on the change time, the optimal procedure alarms when the posterior probability that the change is in effect crosses a threshold.[34](https://www.ssp.ece.upatras.gr/moustakides/downloads/journals/seq2010_1.pdf)\n\n## Applications\n\nChange-point detection originated in industrial quality control, where the goal was to locate a shift in the mean of iid Gaussian variables.[1](https://ar5iv.labs.arxiv.org/html/1801.00718) Bayesian online changepoint detection was demonstrated on well-log data (Gaussian mean changes), Dow Jones returns (variance changes), and coal mining disaster intervals (a Poisson process).[2](https://doi.org/10.48550/arxiv.0710.3742) In genomics, FPOP's cost for copy-number variation detection is competitive with Binary Segmentation while giving more accurate segmentations.[14](https://doi.org/10.1007/s11222-016-9636-3) Other cited applications include systems health monitoring, financial data, climate change, and cyber security,[29](https://proceedings.mlr.press/v202/altamirano23a/altamirano23a.pdf) and, in deep-learning implementations, manufacturing, healthcare, activity monitoring, finance, and environmental monitoring.[35](https://link.springer.com/article/10.1007/s42524-025-4109-z) Li, Fearnhead, Fryzlewicz, and Wang (2024) reported automatic change-point detection via deep learning in the Journal of the Royal Statistical Society Series B,[36](https://doi.org/10.1093/jrsssb/qkae004) and a 2026 Annual Review (Volume 13) highlights change-plane subgroup identification, discontinuities in functional data, and change-point estimation in dynamic networks.[26](https://www.annualreviews.org/content/journals/10.1146/annurev-statistics-041124-044143)\n\n## Limitations and alternatives\n\nAll change-point methods require a threshold, and the choice of threshold is often more important for accuracy than the choice of method.[37](https://onlinelibrary.wiley.com/doi/10.1002/sta4.291) Default thresholds assume iid Gaussian or sub-Gaussian noise; heavier-tailed noise or positive autocorrelation leads to over-estimation of the number of change-points, and methods that estimate segmentations for a range of change-point counts are more reliable when the iid Gaussian assumption fails.[37](https://onlinelibrary.wiley.com/doi/10.1002/sta4.291) Binary Segmentation has low power to detect short segments.[37](https://onlinelibrary.wiley.com/doi/10.1002/sta4.291) Wild binary segmentation overestimates change-point counts for iid errors and becomes dysfunctional with correlated errors; wild contrast maximization handles serial dependence.[16](https://digitalcommons.unl.edu/cgi/viewcontent.cgi?params=/context/statisticsfacpub/article/1167/&path_info=Lund_JC_2023_Good_Practices_and_Common_Pitfalls.pdf) CUSUM requires both pre- and post-change distributions to be parametric and specified exactly, which is restrictive and leaves it non-robust to misspecification.[7](https://par.nsf.gov/servlets/purl/10492374) Page's method can have almost no power against changes less than half the assumed size, and the CUSUM statistic averages post-change data with all prior data, reducing power when a change occurs late in a long run.[18](https://www.jmlr.org/papers/volume24/21-1230/21-1230.pdf) In correlated multiple change-point settings no single method wins; performance depends on the scenario.[38](https://ideas.repec.org/a/eee/csdana/v170y2022ics0167947322000135.html) [Dynamic programming](https://www.edgepedia.org/dynamic-programming) methods often assume uncorrelated series, which is unrealistic in climate applications.[16](https://digitalcommons.unl.edu/cgi/viewcontent.cgi?params=/context/statisticsfacpub/article/1167/&path_info=Lund_JC_2023_Good_Practices_and_Common_Pitfalls.pdf) For regression settings, [Jushan Bai](https://www.edgepedia.org/jushan-bai) and [Pierre Perron](https://www.edgepedia.org/pierre-perron) (1998) developed estimation and testing for linear models with multiple structural changes.[39](https://doi.org/10.2307/2998540)\n\n## References\n\n1. [Selective review of offline change point detection methods](https://ar5iv.labs.arxiv.org/html/1801.00718)\n2. [Adams, Ryan Prescott, MacKay, David J. C. (2007). Bayesian Online Changepoint Detection. arXiv (Cornell University).](https://doi.org/10.48550/arxiv.0710.3742)\n3. [Section 8.3: Change-Point Detection (offline and online) | Building Temporal AI](http://temporalbook.apartsin.com/part-2-classical-forecasting/module-08-anomaly-changepoint/section-8.3.html)\n4. [E. S. PAGE (1954). CONTINUOUS INSPECTION SCHEMES. Biometrika.](https://doi.org/10.1093/biomet/41.1-2.100)\n5. [Optimal detection of changepoints with a linear computational cost (PELT)](https://arxiv.org/pdf/1101.1438v3)\n6. [Piotr Fryzlewicz (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics.](https://doi.org/10.1214/14-aos1245)\n7. [Sequential change-point detection: Computation versus statistical performance](https://par.nsf.gov/servlets/purl/10492374)\n8. [Change-Point Detection and Data Segmentation (book chapter: Detecting a single change-point)](https://ar5iv.labs.arxiv.org/html/2210.07066)\n9. [MATH337: Changepoint Detection (lecture notes)](https://www.lancaster.ac.uk/~romano/teaching/2425MATH337/MATH337--Changepoint-Detection.pdf)\n10. [A note on online change point detection](https://wrap.warwick.ac.uk/id/eprint/189987/1/A%20note%20on%20online%20change%20point%20detection.pdf)\n11. [B. Jackson and colleagues (2005). An algorithm for optimal partitioning of data on an interval. IEEE Signal Processing Letters.](https://doi.org/10.1109/lsp.2001.838216)\n12. [R. Killick, P. Fearnhead, I. A. Eckley (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association.](https://doi.org/10.1080/01621459.2012.737745)\n13. [Univariate mean change point detection: Penalization, CUSUM and optimality](https://wrap.warwick.ac.uk/id/eprint/135155/7/WRAP-Univariate-mean-change-point-Yu-2020.pdf)\n14. [Robert Maidstone and colleagues (2016). On optimal multiple changepoint algorithms for large data. Statistics and Computing.](https://doi.org/10.1007/s11222-016-9636-3)\n15. [Rebecca Killick, Idris A. Eckley (2014). changepoint : An R Package for Changepoint Analysis. Journal of Statistical Software.](https://doi.org/10.18637/jss.v058.i03)\n16. [Good Practices and Common Pitfalls in Climate Time Series Changepoint Techniques: A Review (Lund et al., 2023)](https://digitalcommons.unl.edu/cgi/viewcontent.cgi?params=/context/statisticsfacpub/article/1167/&path_info=Lund_JC_2023_Good_Practices_and_Common_Pitfalls.pdf)\n17. [A Selective Review on Information Criteria in Multiple Change Point Detection (Entropy, 2024)](https://www.mdpi.com/1099-4300/26/1/50)\n18. [Fast Online Changepoint Detection via Functional Pruning CUSUM Statistics (FOCuS)](https://www.jmlr.org/papers/volume24/21-1230/21-1230.pdf)\n19. [Online multivariate changepoint detection: leveraging links with computational geometry | JRSS-B](https://academic.oup.com/jrsssb/article/88/1/171/8223216)\n20. [W. A. Shewhart (1925). The Application of Statistics as an Aid in Maintaining Quality of a Manufactured Product. Journal of the American Statistical Association.](https://doi.org/10.1080/01621459.1925.10502930)\n21. [Abraham Wald (1946). Differentiation Under the Expectation Sign in the Fundamental Identity of Sequential Analysis. The Annals of Mathematical Statistics.](https://doi.org/10.1214/aoms/1177730889)\n22. [E. S. PAGE (1955). A test for a change in a parameter occurring at an unknown point. Biometrika.](https://doi.org/10.1093/biomet/42.3-4.523)\n23. [A. F. M. SMITH (1975). A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika.](https://doi.org/10.1093/biomet/62.2.407)\n24. [Detecting possibly frequent change-points: Wild Binary Segmentation 2 and Steepest Drop to Low Levels](https://stats.lse.ac.uk/fryzlewicz/wbs2/wbs2sdll.pdf)\n25. [A. B. Olshen and colleagues (2004). Circular binary segmentation for the analysis of array-based DNA copy number data. Biostatistics.](https://doi.org/10.1093/biostatistics/kxh008)\n26. [Change-Point Detection and Its Modern Applications (Annual Review of Statistics)](https://www.annualreviews.org/content/journals/10.1146/annurev-statistics-041124-044143)\n27. [Kernel Change-point Analysis (KCpA), NIPS 2008](https://proceedings.neurips.cc/paper_files/paper/2008/file/08b255a5d42b89b0585260b6f2360bdd-Paper.pdf)\n28. [F. Desobry, M. Davy, C. Doncarli (2005). An online kernel change detection algorithm. IEEE Transactions on Signal Processing.](https://doi.org/10.1109/tsp.2005.851098)\n29. 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Econometrica.](https://doi.org/10.2307/2998540)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Statistics and probability › Statistical inference, estimation, sampling, and testing › Hypothesis testing › Sequential tests and stopping-based inference*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/change-point-detection", "markdown_url": "https://www.edgepedia.org/change-point-detection.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Change-point detection\", Edgepedia (EdgeChat), https://www.edgepedia.org/change-point-detection. Edgepedia Community License 1.0.", "credit_md": "\"[Change-point detection](https://www.edgepedia.org/change-point-detection)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/change-point-detection](https://www.edgepedia.org/change-point-detection). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Change-point detection\", Edgepedia (EdgeChat), https://www.edgepedia.org/change-point-detection. Edgepedia Community License 1.0.", "speakable": "Change-point detection comprises statistical methods for identifying when the distribution of a data series changes, using online procedures that alarm quickly or offline procedures that segment the series." }