On the optimality of Bayesian change-point detection
Dong Han, Fugee Tsung, Jinguo Xian
The Annals of Statistics · 2017 · Volume 45 · Issue 4
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.
Keywords
62L10, 62L15, Bayesian change-point detection, Markov process, optimal test
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