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Testing Exchangeability With Martingale for Change-Point Detection

Testing Exchangeability With Martingale for Change-Point Detection

Liang Dai, Mohamed-Rafik Bouguelia
Copyright: © 2021 |Volume: 12 |Issue: 2 |Pages: 20
ISSN: 1941-6237|EISSN: 1941-6245|EISBN13: 9781799860273|DOI: 10.4018/IJACI.2021040101
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MLA

Dai, Liang, and Mohamed-Rafik Bouguelia. "Testing Exchangeability With Martingale for Change-Point Detection." IJACI vol.12, no.2 2021: pp.1-20. http://doi.org/10.4018/IJACI.2021040101

APA

Dai, L. & Bouguelia, M. (2021). Testing Exchangeability With Martingale for Change-Point Detection. International Journal of Ambient Computing and Intelligence (IJACI), 12(2), 1-20. http://doi.org/10.4018/IJACI.2021040101

Chicago

Dai, Liang, and Mohamed-Rafik Bouguelia. "Testing Exchangeability With Martingale for Change-Point Detection," International Journal of Ambient Computing and Intelligence (IJACI) 12, no.2: 1-20. http://doi.org/10.4018/IJACI.2021040101

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Abstract

This work proposes a new exchangeability test for a random sequence through a martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable for designing exchangeability tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions for constructing the additive martingale. By choosing the underlying probability density function of p-values as a betting function, it can be shown that, when a change-point appears, a satisfying trade-off between the smoothness and expected one-step increment of the martingale sequence can be obtained. An online algorithm based on beta distribution parametrization for constructing this betting function is discussed in detail as well.

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