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Bayesian Multiple Change Point Detection in the Presence of Outliers and Its Application to the Magnitude‐Frequency Distributions

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  • Shaochuan Lu
  • Ting Wang

Abstract

Reliable inference of change points that are insensitive to deviations from model assumptions is essential in many real applications. We propose a two‐step iteration algorithm called detection‐pruning algorithm for multiple change point detection in the presence of outliers. In the two‐step iteration algorithm, first, a set of change points is efficiently detected based on a “cleaned” posterior; then, the outliers are explicitly pruned based on the set of change points simulated in the previous step. We use simulation and a real data analysis to demonstrate the effectiveness of the method and apply the method to the magnitude‐frequency distributions of deep earthquakes. We demonstrate the efficient detection of b‐value change points and simultaneously the identification of a complete earthquake catalog with a time‐inhomogeneous completeness threshold for New Zealand deep earthquakes. Implications of the finding are also discussed.

Suggested Citation

  • Shaochuan Lu & Ting Wang, 2025. "Bayesian Multiple Change Point Detection in the Presence of Outliers and Its Application to the Magnitude‐Frequency Distributions," Environmetrics, John Wiley & Sons, Ltd., vol. 36(7), October.
    • Handle: RePEc:wly:envmet:v:36:y:2025:i:7:n:e70044
    DOI: 10.1002/env.70044
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    References listed on IDEAS

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    1. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    2. Paul Fearnhead & Guillem Rigaill, 2019. "Changepoint Detection in the Presence of Outliers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 169-183, January.
    3. Danijel Schorlemmer & Stefan Wiemer & Max Wyss, 2005. "Variations in earthquake-size distribution across different stress regimes," Nature, Nature, vol. 437(7058), pages 539-542, September.
    4. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.
    5. Shaochuan Lu, 2023. "Bayesian multiple changepoint detection with missing data and its application to the magnitude‐frequency distributions," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
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