## The Annals of Statistics

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

### On the optimality of Bayesian change-point detection

Dong Han, Fugee Tsung, and Jinguo Xian

#### 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**

https://projecteuclid.org/euclid.aos/1498636860

**Digital Object Identifier**

doi:10.1214/16-AOS1479

**Mathematical Reviews number (MathSciNet)**

MR3670182

**Zentralblatt MATH identifier**

1378.62041

**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. https://projecteuclid.org/euclid.aos/1498636860

#### 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-AOS1479SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.