ON THE OPTIMALITY OF BAYESIAN CHANGE-POINT DETECTION

• 成果类型: Article
• 署名作者: Han, Dong; Tsung, Fugee; Xian, Jinguo
• 署名单位: Shanghai Jiao Tong University; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1479
• 发表日期: 2017
• 页码: 1375-1402
• 关键词: shiryaev-roberts procedure

摘要

By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian changepoint 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.