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On‐line inference for multiple changepoint problems

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  • Paul Fearnhead
  • Zhen Liu

Abstract

Summary. We propose an on‐line algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations, at the expense of introducing small errors, and we propose two new, optimum resampling algorithms for this problem. One, a version of rejection control, allows the particle filter to choose the number of particles that are required at each time step automatically. The new resampling algorithms substantially outperform standard resampling algorithms on examples that we consider; and we demonstrate how the resulting particle filter is practicable for segmentation of human G+C content.

Suggested Citation

  • Paul Fearnhead & Zhen Liu, 2007. "On‐line inference for multiple changepoint problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 589-605, September.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:589-605
    DOI: 10.1111/j.1467-9868.2007.00601.x
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    Cited by:

    1. Eric Ruggieri, 2018. "A pruned recursive solution to the multiple change point problem," Computational Statistics, Springer, vol. 33(2), pages 1017-1045, June.
    2. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2020. "Modeling Turning Points In Global Equity Market," DEM Working Papers Series 195, University of Pavia, Department of Economics and Management.
    3. Chen, Yudong & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional, multiscale online changepoint detection," LSE Research Online Documents on Economics 113665, London School of Economics and Political Science, LSE Library.
    4. Chao Du & Chu-Lan Michael Kao & S. C. Kou, 2016. "Stepwise Signal Extraction via Marginal Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 314-330, March.
    5. Robert C Wilson & Matthew R Nassar & Joshua I Gold, 2013. "A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems," PLOS Computational Biology, Public Library of Science, vol. 9(7), pages 1-18, July.
    6. Yukio Ohsawa & Teruaki Hayashi & Takaaki Yoshino, 2019. "Tangled String for Multi-Scale Explanation of Contextual Shifts in Stock Market," Papers 1901.09469, arXiv.org.
    7. Stein Olav Skrøvseth & Johan Gustav Bellika & Fred Godtliebsen, 2012. "Causality in Scale Space as an Approach to Change Detection," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-14, December.
    8. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    9. Tian, Guo-Liang & Ng, Kai Wang & Li, Kai-Can & Tan, Ming, 2009. "Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3314-3323, July.
    10. Hinoveanu, Laurentiu C. & Leisen, Fabrizio & Villa, Cristiano, 2019. "Bayesian loss-based approach to change point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 61-78.
    11. Rui Qiang & Eric Ruggieri, 2023. "Autocorrelation and Parameter Estimation in a Bayesian Change Point Model," Mathematics, MDPI, vol. 11(5), pages 1-22, February.
    12. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    13. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, June.
    14. Thies, Sven & Molnár, Peter, 2018. "Bayesian change point analysis of Bitcoin returns," Finance Research Letters, Elsevier, vol. 27(C), pages 223-227.
    15. Jian He & Asma Khedher & Peter Spreij, 2021. "A Kalman particle filter for online parameter estimation with applications to affine models," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 353-403, July.
    16. Ricardo C. Pedroso & Rosangela H. Loschi & Fernando Andrés Quintana, 2023. "Multipartition model for multiple change point identification," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 759-783, June.
    17. Yixiao Li & Gloria Lin & Thomas Lau & Ruochen Zeng, 2019. "A Review of Changepoint Detection Models," Papers 1908.07136, arXiv.org.
    18. Ruggieri, Eric & Antonellis, Marcus, 2016. "An exact approach to Bayesian sequential change point detection," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 71-86.
    19. Sang Gil Kang & Woo Dong Lee & Yongku Kim, 2021. "Bayesian Multiple Change-Points Detection in a Normal Model with Heterogeneous Variances," Computational Statistics, Springer, vol. 36(2), pages 1365-1390, June.
    20. Haipeng Xing & Hongsong Yuan & Sichen Zhou, 2017. "A Mixtured Localized Likelihood Method for GARCH Models with Multiple Change-points," Review of Economics & Finance, Better Advances Press, Canada, vol. 8, pages 44-60, May.
    21. Seong W. Kim & Sabina Shahin & Hon Keung Tony Ng & Jinheum Kim, 2021. "Binary segmentation procedures using the bivariate binomial distribution for detecting streakiness in sports data," Computational Statistics, Springer, vol. 36(3), pages 1821-1843, September.
    22. Yukio Ohsawa, 2018. "Graph-Based Entropy for Detecting Explanatory Signs of Changes in Market," The Review of Socionetwork Strategies, Springer, vol. 12(2), pages 183-203, December.

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