版本2（2026年）新增说明：本文已被替代。本文计算的每个索引为最近变点的概率，是贝叶斯在线变点检测（R. P. Adams和D. J. C. MacKay，arXiv:0710.3742，2007）的游程后验概率，该概率可被精确且高效地计算；另见P. Fearnhead，《统计与计算》16:203-213，2006。本文结果所用的实现存在错误，因此这些结果不可靠。修正后的实现、测试及错误说明位于此https URL。本文其余部分与版本1一致。我们提出一种用于同时检测和定位时间序列中变点的算法，以及用于预测序列下一个点分布的框架。该算法的核心是一组方程，可为每个索引i计算最近变点发生在i处的概率。我们通过将该算法应用于变点检测问题，并与广义似然比（GLR）算法进行比较来评估它。我们发现，在广泛的场景中，我们的算法与GLR算法性能相当或更优，且随着信噪比降低，优势会增大。
英文摘要：
Note added in version 2 (2026): this paper has been superseded. The probability it computes, that each index is the most recent changepoint, is the run-length posterior of Bayesian online changepoint detection (R. P. Adams and D. J. C. MacKay, arXiv:0710.3742, 2007), which computes it exactly and efficiently; see also P. Fearnhead, Statistics and Computing 16:203-213, 2006. The implementation used for the results in this paper contained errors, so those results should not be relied on. A corrected implementation, tests, and a description of the errors are at https://github.com/AllenDowney/ChangePoint. The rest of the paper is unchanged from version 1.
We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i. We evaluate this algorithm by applying it to the change point detection problem and comparing it to the generalized likelihood ratio (GLR) algorithm. We find that our algorithm is as good as GLR, or better, over a wide range of scenarios, and that the advantage increases as the signal-to-noise ratio decreases.
By attaching auxiliary event times to the chronologically ordered observations, we formulate the Bayesian multiple changepoint problem of discrete-time observations into that of continuous-time ones. A version of forward-filtering backward-sampling (FFBS) algorithm is proposed for the simulation of changepoints within a collapsed Gibbs sampling scheme. Ideally, both the computational cost and memory cost of the FFBS algorithm can be quadratically scaled down to the number of changepoints, instead of the number of observations, which is otherwise prohibitive for a long sequence of observations.…
Recent findings suggest that abnormal operating conditions of equipment in the oil and gas supply chain represent a large fraction of anthropogenic methane emissions. Thus, effective mitigation of emissions necessitates rapid identification and repair of sources caused by faulty equipment. In addition to advances in sensing technology that allow for more frequent surveillance, prompt and cost-effective identification of sources requires computational frameworks that provide automatic fault detection. Here, we present a changepoint detection algorithm based on a recursive Bayesian scheme that a…
Near real time change detection is important for a variety of Earth monitoring applications and remains a high priority for remote sensing science. Data sparsity, subtle changes, seasonal trends, and the presence of outliers make detecting actual landscape changes challenging. Adams and MacKay (2007) introduced Bayesian Online Changepoint Detection (BOCPD), a computationally efficient, exact Bayesian method for change detection. Incorporation of prior information allows for relaxed dependence on dense data and an extensive stable period, making this method applicable to relatively short time s…
Princeton University（普林斯顿大学）；Arm ML Research Lab（Arm机器学习研究实验室）
Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it may be beneficial to trade the cost of collecting an environmental measurement against the quality or "fidelity" of this measurement and how the measurement affects changepoint estimation. For instance, one might decide between inertial measurements or GPS to determine changepoints for motion. A Bayesian approach to changepoint detection is particularly appe…
In regression models, predictor variables with inherent ordering, such as tumor staging ranging and ECOG performance status, are commonly seen in medical settings. Statistically, it may be difficult to determine the functional form of an ordinal predictor variable. Often, such a variable is dichotomized based on whether it is above or below a certain cutoff. Other methods conveniently treat the ordinal predictor as a continuous variable and assume a linear relationship with the outcome. However, arbitrarily choosing a method may lead to inaccurate inference and treatment. In this paper, we pro…
A Bayesian changepoint methodology for high dimensional multivariate time series and space-time data: A study of structural change using remotely sensed data
We provide an online framework for analyzing data recorded by smart watches during running activities. In particular, we focus on identifying variations in the behavior of one or more measurements caused by changes in physical condition, such as physical discomfort, periods of prolonged de-training, or even the malfunction of measuring devices. Our framework considers data as a sequence of running activities represented by multivariate time series of physical and biometric data. We combine classical changepoint detection models with an unknown number of components with Gaussian state space mod…
Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve changepoint detection problem using fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical pr…
Changepoint Detection in Categorical Time Series with Application to Daily Total Cloud Cover in Canada
University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）；Virginia Commonwealth University（弗吉尼亚联邦大学）；Climate Research Division, Science and Technology Branch, Environment and Climate Change Canada（加拿大环境与气候变化部科技处气候研究司）
Motivated by a condition monitoring application arising from subsea engineering we derive a novel, scalable approach to detecting anomalous mean structure in a subset of correlated multivariate time series. Given the need to analyse such series efficiently we explore a computationally efficient approximation of the maximum likelihood solution to the resulting modelling framework, and develop a new dynamic programming algorithm for solving the resulting Binary Quadratic Programme when the precision matrix of the time series at any given time-point is banded. Through a comprehensive simulation s…
This paper presents a statistical analysis of structural changes in the Central England temperature series, one of the longest surface temperature records available. A changepoint analysis is performed to detect abrupt changes, which can be regarded as a preliminary step before further analysis is conducted to identify the causes of the changes (e.g., artificial, human-induced or natural variability). Regression models with structural breaks, including mean and trend shifts, are fitted to the series and compared via two commonly used multiple changepoint penalized likelihood criteria that bala…
We introduce PyChEst, a Python package which provides tools for the simultaneous estimation of multiple changepoints in the distribution of piece-wise stationary time series. The nonparametric algorithms implemented are provably consistent in a general framework: when the samples are generated by unknown piece-wise stationary processes. In this setting, samples may have long-range dependencies of arbitrary form and the finite-dimensional marginals of any (unknown) fixed size before and after the changepoints may be the same. The strength of the algorithms included in the package is in their ab…
