changepoint.bib

@article{Killick2013,
abstract = {One of the key challenges in changepoint analysis is the ability to detect multiple changes within a given time series or sequence. The changepoint package has been developed to provide users with a choice of multiple changepoint search methods to use in conjunction with a given changepoint method and in particular provides an implementation of the recently proposed PELT algorithm. This article describes the search methods which are implemented in the package as well as some of the available test statistics whilst highlighting their application with simulated and practical examples. segmentation, break points, search methods},
archivePrefix = {arXiv},
arxivId = {arXiv:1501.0228},
author = {Killick, Rebecca and Eckley, Ia},
doi = {10.1359/JBMR.0301229},
eprint = {arXiv:1501.0228},
file = {:Users/julianflowers/Downloads/v58i03.pdf:pdf},
isbn = {9781439811870},
issn = {1548-7660},
journal = {Lancaster University},
number = {3},
pages = {1--15},
pmid = {18291371},
title = {{changepoint: An R Package for changepoint analysis}},
url = {https://www.jstatsoft.org/article/view/v058i03/v58i03.pdf},
volume = {58},
year = {2013}
}
@article{Eckley2011,
abstract = {Many time series are characterised by abrupt changes in structure, such as sudden jumps in level or volatility. We consider change points to be those time points which divide a data set into distinct homogeneous segments. In practice the number of change points will not be known. The ability to detect changepoints are important for both methodological and practical reasons including: the validation of an untested scientific hypothesis (e.g. Henderson and Matthews, 1993); monitoring and assessment of safety critical pro-cesses (e.g. Elsner et al., 2004); and the validation of modelling assumptions (e.g. Fryzlewicz and Subba Rao, 2009). The development of inference methods for change point problems is by no means a recent phenomenon, with early works including Page (1954a), Shiryaev (1963) and Hinkley (1970). Increasingly the ability to detect change points quickly and accu-rately is of interest to a wide range of disciplines. Recent examples of application areas include numerous bioinformatic applications (Lio and Vannucci, 2000; Erdman and Emerson, 2008) the detection of malware within software (Yan et al., 2008), network traffic analysis (Kwon et al., 2006), finance (Spokoiny, 2009), climatology (Jaxk et al., 2007) and oceanography (Killick et al., 2009). In this chapter we describe and compare a number of different approaches for estimating changepoints. For a more general overview of changepoint methods, we refer interested readers to Carlstein et al. (1994) and Chen and Gupta (2000). The structure of this chapter is as follows. First we introduce the model we fo-cus on. We then describe methods for detecting a single changepoint and methods for detecting multiple changepoints, which will cover both frequentist and Bayesian approaches. For multiple changepoint models the computational challenge of per-forming inference is to deal with the large space of possible sets of changepoint positions. We describe algorithms that, for the class of models we consider, can perform inference exactly even for large data sets. In Section 1.4 we look at prac-tical issues of implementing these methods, and compare the different approaches, through a detailed simulation study. Our study is based around the problem of detecting changes in the covariance structure of a time-series, and results suggest that Bayesian methods are more suitable for detection of changepoints, particularly for multiple changepoint applications. The study also demonstrates the advantage of using the exact inference methods. We end with a discussion. Within this chapter we consider the following changepoint models. Let us assume we have time-series data, y 1:n = (y 1 , . . . , y n). For simplicity we assume the obser-vation at each time t, y t , is univariate – though extensions to multivariate data are straightforward. Our model will have a number of changepoints, m, together with their positions, $\tau$ 1:m = ($\tau$ 1 , . . . , $\tau$ m). Each changepoint position is an integer between 1 and n − 1 inclusive. We define $\tau$ 0 = 0 and $\tau$ m+1 = n, and assume that the changepoints are ordered so that $\tau$ i {\textless} $\tau$ j if and only if i {\textless} j. The m changepoints will split the data into m + 1 segments. The ith segment will consist of data y $\tau$i−1+1:$\tau$i . For each segment there will be a set of parameters; the parameters associated with the ith segment will be denoted $\theta$ i . We will write the likelihood function as L(m, $\tau$ 1:m , $\theta$ 1:m+1) = p(y 1:n |m, $\tau$ 1:m , $\theta$ 1:m+1).},
author = {Eckley, I.A. and Fearnhead, P. and Killick, R.},
doi = {10.1017/CBO9780511984679.011},
isbn = {9780511984679},
journal = {Bayesian Time Series Models},
number = {January},
pages = {205--224},
title = {{Analysis of Changepoint Models}},
year = {2011}
}
@article{Adams2007,
abstract = {Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, most Bayesian papers have focused on the retrospective segmentation problem. Here we examine the case where the model parameters before and after the changepoint are independent and we derive an online algorithm for exact inference of the most recent changepoint. We compute the probability distribution of the length of the current ``run,'' or time since the last changepoint, using a simple message-passing algorithm. Our implementation is highly modular so that the algorithm may be applied to a variety of types of data. We illustrate this modularity by demonstrating the algorithm on three different real-world data sets.},
archivePrefix = {arXiv},
arxivId = {0710.3742},
author = {Adams, Ryan Prescott and Mackay, David J. C.},
doi = {arXiv:0710.3742v1},
eprint = {0710.3742},
isbn = {9781509028337},
journal = {arXiv.org},
pages = {7},
title = {{Bayesian Online Changepoint Detection}},
url = {http://arxiv.org/abs/0710.3742},
year = {2007}
}
@article{Li2015,
abstract = {AbstractThis paper examines multiple changepoint detection procedures that use station history (metadata) information. Metadata records are available for some climate time series; however, these records are notoriously incomplete and many station moves and gauge changes are unlisted (undocumented). The shift in a series must be comparatively larger to declare a changepoint at an undocumented time. Also, the statistical methods for the documented and undocumented scenarios radically differ: a simple t test adequately detects a single mean shift at a documented changepoint time, while a tmax distribution is appropriate for a single undocumented changepoint analysis. Here, the multiple changepoint detection problem is considered via a Bayesian approach, with the metadata record being used to formulate a prior distribution of the changepoint numbers and their location times. This prior distribution is combined with the data to obtain a posterior distribution of changepoint numbers and location times. Estimate...},
author = {Li, Yingbo and Lund, Robert},
doi = {10.1175/JCLI-D-14-00442.1},
isbn = {08948755},
issn = {0894-8755},
journal = {Journal of Climate},
number = {10},
pages = {4199--4216},
pmid = {102621234},
title = {{Multiple Changepoint Detection Using Metadata}},
url = {http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00442.1},
volume = {28},
year = {2015}
}
@misc{Killick2012,
abstract = {Implements various mainstream and specialised changepoint methods for finding sin- gle and multiple changepoints within data. Many popular non-parametric and frequentist meth- ods are included. The cpt.mean, cpt.var, cpt.meanvar functions should be your first point of call.},
author = {Killick, Rebecca and Eckley, Idris A},
booktitle = {Lancaster University},
pages = {1--128},
title = {{Package ‘ changepoint '}},
url = {http://www.lancs.ac.uk/{~}killick/Pub/KillickEckley2011.pdf{\%}5Cnhttp://www.lancs.ac.uk/{\%}7B{~}{\%}7Dkillick/Pub/KillickEckley2011.pdf},
year = {2012}
}
@article{Hawkins2003,
abstract = {Statistical process control (SPC) requires statistical methodologies that detect changes in the pattern of data over time. The common methodologies, such as Shewhart, cumulative sum (cusum), and exponentially weighted moving average (EWMA) charting, require the in-control values of the process parameters, but these are rarely known accurately. Using estimated parameters, the run length behavior changes randomly from one realization to another, making it impossible to control the run length behavior of any particular chart. A suitable methodology for detecting and diagnosing step changes based on imperfect process knowledge is the unknown-parameter changepoint formulation. Long recognized as a Phase I analysis tool, we argue that it is also highly effective in allowing the user to progress seamlessly from the start of Phase I data gathering through Phase II SPC monitoring. Despite not requiring specification of the post-change process parameter values, its performance is never far short of that of the optimal cusum chart which requires this knowledge, and it is far superior for shifts away from the cusum shift for which the cusum chart is optimal. As another benefit, while changepoint methods are designed for step changes that persist, they are also competitive with the Shewhart chart, the chart of choice for isolated non-sustained special causes.},
author = {Hawkins, Douglas M. and Qiu, Peihua and Chang, Wook Kang},
isbn = {0022-4065},
journal = {Journal of Quality Technology},
number = {4},
pages = {355--366},
title = {{The changepoint model for statistical process control}},
url = {http://cat.inist.fr/?aModele=afficheN{\&}cpsidt=15174770},
volume = {35},
year = {2003}
}