大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Asymptotic Theory of Sequential Change Detection and Identification

山崎和俊（大阪大学金融・保険教育研究センター）

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4. Asymptotic Theory of Sequential Change Detection and Identification

大阪大学 金融・保険セミナーシリーズ 第24回

Asymptotic Theory of Sequential Change Detection and Identification

山崎和俊（大阪大学金融・保険教育研究センター）

We study the joint problem of change point detection and
sequential multiple hypothesis testing. Based on a sequence of observations, one needs to detect a sudden and unobservable change at the earliest and identify its cause accurately. We propose a sequential decision strategy that triggers an alarm when the posterior probability of a certain type of change exceeds some threshold for the first time. We show its asymptotic optimalities under the Bayes risk and the fixed-error formulations as the unit cost of detection delay and the probability of a misdiagnosis go to zero, respectively. We verify the results numerically using an example where the observation process is normally distributed.