The Annals of Statistics

On the optimality of Bayesian change-point detection

Dong Han, Fugee Tsung, and Jinguo Xian

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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.

Article information

Source
Ann. Statist. Volume 45, Number 4 (2017), 1375-1402.

Dates
Received: October 2015
Revised: August 2016
First available in Project Euclid: 28 June 2017

Permanent link to this document
http://projecteuclid.org/euclid.aos/1498636860

Digital Object Identifier
doi:10.1214/16-AOS1479

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60]

Keywords
Optimal test Bayesian change-point detection Markov process

Citation

Han, Dong; Tsung, Fugee; Xian, Jinguo. On the optimality of Bayesian change-point detection. Ann. Statist. 45 (2017), no. 4, 1375--1402. doi:10.1214/16-AOS1479. http://projecteuclid.org/euclid.aos/1498636860.


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References

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Supplemental materials

  • Supplement A: Proofs of Theorem 4 of the paper “On the optimality of Bayesian change-point detection”. We prove in the supplementary material that the optimal (minimal) average detection delay is equal to 1 for any (possibly large) average run length to false alarm if the number of possible change-points is finite for observations being a Markov process.
    Digital Object Identifier: doi:10.1214/16-AOS1479SUPP
    Supplemental files available for subscribers.

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