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Online change detection of Markov chains with unknown post-change transition probabilities

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  • Jin-Guo Xian
  • Dong Han
  • Jian-Qi Yu

Abstract

In this paper, we investigate the performance of cumulative sum (CUSUM) stopping rules for the online detection of unknown change point in a time homogeneous Markov chain. Under the condition that the post-change transition probabilities are unknown, we proposed two CUSUM type schemes for the detection. The first scheme is based on the maximum likelihood estimates of the post-change transition probabilities. This scheme is limited by its computation burden, which is mitigated by another scheme based on the reference transition probabilities selected from a prior known region. We give the bounds of the mean delay time and the mean time between false alarms to illustrate the effectiveness of the proposed schemes. The results of the simulation also demonstrate the feasibility of the proposed schemes.

Suggested Citation

  • Jin-Guo Xian & Dong Han & Jian-Qi Yu, 2016. "Online change detection of Markov chains with unknown post-change transition probabilities," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 597-611, February.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:3:p:597-611
    DOI: 10.1080/03610926.2013.833243
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    Cited by:

    1. Guglielmo D'Amico & Filippo Petroni & Philippe Regnault & Stefania Scocchera & Loriano Storchi, 2019. "A copula based Markov Reward approach to the credit spread in European Union," Papers 1902.00691, arXiv.org.
    2. Damásio, Bruno & Nicolau, João, 2024. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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