Quickest detection with exponential penalty for delay

• 成果类型: Article
• 署名作者: Poor, HV
• 署名单位: Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 2179-2205
• 关键词: cusum procedure; times

摘要

The problem of detecting a change in the probability distribution of a random sequence is considered. Stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria. In both cases, the detection delay is penalized exponentially rather than Linearly, as has been the case in previous formulations of this problem. The first of these two criteria is to minimize a worst-case measure of the exponential detection delay within a lower-bound constraint on the mean time between false alarms. Expressions for the performance of the optimal detection rule are also developed for this case. It is seen, for example, that the classical Page CUSUM test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty. The second criterion considered is a Bayesian one, in which the unknown change point is assumed to obey a geometric prior distribution. In this case, the optimal stopping time effects an optimal trade-off between the expected exponential detection delay and the probability of false alarm. Finally, generalizations of these results to problems in which the penalties for delay may be path dependent are also considered.