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One of the contemporary challenges in anomaly detection is the ability to detect, and differentiate between, both point and collective anomalies within a data sequence or time series. The anomaly package has been developed to provide users with a choice of anomaly detection methods and, in particular, provides an implementation of the recently proposed Collective And Point Anomaly family of anomaly detection algorithms. This article describes the methods implemented whilst also highlighting their application to simulated data as well as real data examples contained in the package., Comment: 24 pages, 6 figures. An R package that implements the methods discussed in the paper can be obtained from The Comprehensive R Archive Network (CRAN) via https://cran.r-project.org/web/packages/anomaly/index.html

The ability to quickly and accurately detect anomalous structure within data sequences is an inference challenge of growing importance. This work extends recently proposed post-hoc (offline) anomaly detection methodology to the sequential setting. The resultant procedure is capable of real-time analysis and categorisation between baseline and two forms of anomalous structure: point and collective anomalies. Various theoretical properties of the procedure are derived. These, together with an extensive simulation study, highlight that the average run length to false alarm and the average detection delay of the proposed online algorithm are very close to that of the offline version. Experiments on simulated and real data are provided to demonstrate the benefits of the proposed method.

Detecting recent changepoints in time-series can be important for short-term prediction, as we can then base predictions just on the data since the changepoint. In many applications we have panel data, consisting of many related univariate time-series. We present a novel approach to detect sets of most recent changepoints in such panel data which aims to pool information across time-series, so that we preferentially infer a most recent change at the same time-point in multiple series. Our approach is computationally efficient as it involves analysing each time-series independently to obtain a profile likelihood like quantity that summarises the evidence for the series having either no change or a specific value for its most recent changepoint. We then post-process this output from each time-series to obtain a potentially small set of times for the most recent changepoints, and, for each time, the set of series which has their most recent changepoint at that time. We demonstrate the usefulness of this method on two data sets: forecasting events in a telecommunications network and inference about changes in the net asset ratio for a panel of US firms.

We present a novel Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the possibility that such changes will only be present in a, potentially small, subset of the time-series. We develop a general model for this problem, and show how it is possible to accurately and efficiently perform Bayesian inference, based upon recursions that enable independent sampling from the posterior distribution. A motivating application for this problem comes from detecting copy number variation (CNVs), using data from multiple individuals. Pooling information across individuals can increase the power of detecting CNVs, but often a specific CNV will only be present in a small subset of the individuals. We evaluate the Bayesian method on both simulated and real CNV data, and give evidence that this approach is more accurate than a recently proposed method for analysing such data.