Bayesian Detection of Abnormal Segments in Multiple Time Series

Lawrence Bardwell; Paul Fearnhead

doi:10.1214/16-BA998

Bayesian Analysis

Bayesian Anal.
Volume 12, Number 1 (2017), 193-218.

Bayesian Detection of Abnormal Segments in Multiple Time Series

Lawrence Bardwell and Paul Fearnhead

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Abstract

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.

Article information

Source
Bayesian Anal., Volume 12, Number 1 (2017), 193-218.

Dates
First available in Project Euclid: 23 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ba/1456235761

Digital Object Identifier
doi:10.1214/16-BA998

Mathematical Reviews number (MathSciNet)
MR3597572

Zentralblatt MATH identifier
1384.62286

Keywords
BARD changepoint detection copy number variation PASS

Citation

Bardwell, Lawrence; Fearnhead, Paul. Bayesian Detection of Abnormal Segments in Multiple Time Series. Bayesian Anal. 12 (2017), no. 1, 193--218. doi:10.1214/16-BA998. https://projecteuclid.org/euclid.ba/1456235761

References

Bardwell, L. and Fearnhead, P. (2016). “Supplementary Material of “Bayesian detection of abnormal segments in multiple time series”.” Bayesian Analysis.
Barry, D. and Hartigan, J. A. (1992). “Product partition models for change point problems.” The Annals of Statistics, 20(1): 260–279. http://www.jstor.org/stable/2242159.
Zentralblatt MATH: 0780.62071
Digital Object Identifier: doi:10.1214/aos/1176348521
Project Euclid: euclid.aos/1176348521
Berger, J. (1985). Statistical decision theory and Bayesian analysis. Springer series in statistics. New York, NY [u.a.]: Springer, 2. ed edition. http://gso.gbv.de/DB=2.1/CMD?ACT=SRCHA&SRT=YOP&IKT=1016&TRM=ppn+027440176&sourceid=fbw_bibsonomy
Carter, C. K. and Kohn, R. (1994). “On Gibbs sampling for state space models.” Biometrika, 81(3): 541–553.
Zentralblatt MATH: 0809.62087
Digital Object Identifier: doi:10.1093/biomet/81.3.541
Cox, D. (1962). Renewal Theory. Methuen’s monographs on applied probability and statistics. Methuen. http://books.google.co.uk/books?id=0VxRAAAAMAAJ.
Fearnhead, P. (2006). “Exact and efficient Bayesian inference for multiple changepoint problems.” Statistics and Computing, 16(2): 203–213. http://www.springerlink.com/content/51j72n7476l1011q/.
Fearnhead, P. and Liu, Z. (2007). “On-line inference for multiple changepoint problems.” Journal of the Royal Statistical Society B, 69: 589–605. http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2007.00601.x/abstract.
Fearnhead, P. and Vasileiou, D. (2009). “Bayesian analysis of isochores.” Journal of the American Statistical Association, 104(485): 132–141. http://pubs.amstat.org/doi/abs/10.1198/jasa.2009.0009?journalCode=jasa.
Mathematical Reviews (MathSciNet): MR2663038
Zentralblatt MATH: 06448238
Digital Object Identifier: doi:10.1198/jasa.2009.0009
Frick, K., Munk, A., and Sieling, H. (2014). “Multiscale change point inference.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(3): 495–580. http://dx.doi.org/10.1111/rssb.12047.
Galeano, P., Peña, D., and Tsay, R. S. (2006). “Outlier detection in multivariate time series by projection pursuit.” Journal of the American Statistical Association, 101(474): 654–669. http://www.jstor.org/stable/27590725.
Zentralblatt MATH: 1119.62360
Digital Object Identifier: doi:10.1198/016214505000001131
Jandhyala, V., Fotopoulos, S., MacNeill, I., and Liu, P. (2013). “Inference for single and multiple change-points in time series.” Journal of Time Series Analysis.
Mathematical Reviews (MathSciNet): MR3070866
Zentralblatt MATH: 1275.62061
Digital Object Identifier: doi:10.1111/jtsa.12035
Jeng, X. J., Cai, T. T., and Li, H. (2013). “Simultaneous discovery of rare and common segment variants.” Biometrika, 100(1): 157–172. http://www.biomedsearch.com/nih/Simultaneous-Discovery-Rare-Common-Segment/23825436.html.
Zentralblatt MATH: 1284.62658
Digital Object Identifier: doi:10.1093/biomet/ass059
Jin, J. (2004). Detecting a Target in Very Noisy Data from Multiple Looks, volume 45 of Lecture Notes – Monograph Series, 255–286. Beachwood, Ohio, USA: Institute of Mathematical Statistics. http://dx.doi.org/10.1214/lnms/1196285396.
Kulkarni, V. (2012). Introduction to Modeling and Analysis of Stochastic Systems. Springer Texts in Statistics. Springer London, Limited. http://books.google.co.uk/books?id=2EeGkQEACAAJ.
Levine, R. A. and Casella, G. (2001). “Implementations of the Monte Carlo EM Algorithm.” Journal of Computational and Graphical Statistics, 10(3): 422–439.
Olshen, A. B., Venkatraman, E. S., Lucito, R., and Wigler, M. (2004). “Circular binary segmentation for the analysis of array based DNA copy number data.” Biostatistics, 5(4): 557–572. http://biostatistics.oxfordjournals.org/content/5/4/557.abstract.
Zentralblatt MATH: 1155.62478
Digital Object Identifier: doi:10.1093/biostatistics/kxh008
Pinto, D., Darvishi, K., Shi, X., Rajan, D., Rigler, D., Fitzgerald, T., Lionel, A. C., Thiruvahindrapuram, B., MacDonald, J. R., Mills, R., Prasad, A., Noonan, K., Gribble, S., Prigmore, E., Donahoe, P. K., Smith, R. S., Park, J. H., Hurles, M. E., Carter, N. P., Lee, C., Scherer, S. W., and Feuk, L. (2011). “Comprehensive assessment of array-based platforms and calling algorithms for detection of copy number variants.” Nature Biotechnology, 29(6): 512–521.
Qu, G., Hariri, S., and Yousif, M. (2005). “Multivariate statistical analysis for network attacks detection.” In The 3rd ACS/IEEE International Conference on Computer Systems and Applications, 2005, 9.
Siegmund, D., Yakir, B., and Zhang, N. R. (2011). “Detecting simultaneous variant intervals in aligned sequences.” The Annals of Applied Statistics, 5(2A): 645–668.
Zentralblatt MATH: 1223.62166
Digital Object Identifier: doi:10.1214/10-AOAS400
Spiegel, S., Gaebler, J., Lommatzsch, A., De Luca, E., and Albayrak, S. (2011). “Pattern recognition and classification for multivariate time series.” In Proceedings of the Fifth International Workshop on Knowledge Discovery from Sensor Data, SensorKDD’11, 34–42. New York, NY, USA: ACM. http://doi.acm.org/10.1145/2003653.2003657.
Tsay, R. S., Peña, D., and Pankratz, A. E. (2000). “Outliers in multivariate time series.” Biometrika, 87(4): 789–804. http://biomet.oxfordjournals.org/content/87/4/789.abstract.
Zentralblatt MATH: 1028.62073
Digital Object Identifier: doi:10.1093/biomet/87.4.789
Wyse, J., Friel, N., and Rue, H. (2011). “Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments.” Bayesian Analysis, 6(4): 501–528.
Zentralblatt MATH: 1330.62160
Digital Object Identifier: doi:10.1214/11-BA620
Yau, C. and Holmes, C. C. (2010). “A decision theoretic approach for segmental classification using Hidden Markov models.” http://arxiv.org/abs/1007.4532
Zhang, N. (2010). “DNA copy number profiling in normal and tumor genomes.” In Feng, J., Fu, W., and Sun, F. (eds.), Frontiers in Computational and Systems Biology, volume 15 of Computational Biology, 259–281. Springer London. http://dx.doi.org/10.1007/978-1-84996-196-7_14.
Zhang, N. R., Siegmund, D. O., Ji, H., and Li, J. Z. (2010). “Detecting simultaneous changepoints in multiple sequences.” Biometrika, 97(3): 631–645. http://ideas.repec.org/a/oup/biomet/v97y2010i3p631-645.html.
Zentralblatt MATH: 1195.62168
Digital Object Identifier: doi:10.1093/biomet/asq025

Supplemental materials

Supplementary Material of “Bayesian detection of abnormal segments in multiple time series”.
Digital Object Identifier: doi:10.1214/16-BA998SUPP
Supplemental PDF (186 KB)

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Bayesian Detection of Abnormal Segments in Multiple Time Series

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