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August 2017 On the optimality of Bayesian change-point detection
Dong Han, Fugee Tsung, Jinguo Xian
Ann. Statist. 45(4): 1375-1402 (August 2017). DOI: 10.1214/16-AOS1479

Abstract

By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian change-point detection not only for a general prior distribution of change-points but also for observations being a Markov process. Moreover, the optimal (minimal) average detection delay is proved to be equal to $1$ for any (possibly large) average run length to false alarm if the number of possible change-points is finite.

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Dong Han. Fugee Tsung. Jinguo Xian. "On the optimality of Bayesian change-point detection." Ann. Statist. 45 (4) 1375 - 1402, August 2017. https://doi.org/10.1214/16-AOS1479

Information

Received: 1 October 2015; Revised: 1 August 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 1378.62041
MathSciNet: MR3670182
Digital Object Identifier: 10.1214/16-AOS1479

Subjects:
Primary: 62L10
Secondary: 62L15

Keywords: Bayesian change-point detection , Markov process , optimal test

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 4 • August 2017
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