The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-vs.-"false-positive"-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cyclic setup, the so-called Shiryaev-Roberts (SR) detection procedure is known to be the "best one can do", provided, however, that the observations' pre- and post-change distributions are both fully specified. We consider a more realistic setup, viz. one where the post-change distribution is assumed known only up to a parameter, so that the latter may be "misspecified". The question of interest is the sensitivity (or robustness) of the otherwise "best" SR procedure with respect to a possible misspecification of the post-change distribution parameter. To answer this question, we provide a case study where, in a specific Gaussian scenario, we allow the SR procedure to be "out of tune" in the way of the post-change distribution parameter, and numerically assess the effect of the "mistuning" on Shiryaev's (multi-cyclic) Stationary Average Detection Delay delivered by the SR procedure. The comprehensive quantitative robustness characterization of the SR procedure obtained in the study can be used to develop the respective theory as well as to provide a rational for practical design of the SR procedure. The overall qualitative conclusion of the study is an expected one: the SR procedure is less (more) robust for less (more) contrast changes and for lower (higher) levels of the false alarm risk.
An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations
Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection
Cherkasy State Business College（切尔卡瑟国立商业学院）；State Scientific Research Institute of Armament and Military Equipment（国家军事装备科学研究所）；Testing and Certification, Cherkasy, Ukraine（乌克兰切尔卡瑟测试与认证中心）；Uzhhorod National University（乌日霍罗德国立大学）
Change Detection in Probability Flow ODE: Online Testing in Diffusion Latent Spaces
National Research University Higher School of Economics（国立研究型大学高等经济学院）；The University of Sydney Business School（悉尼大学商学院）；CIREQ（蒙特利尔数量经济学研究中心）；CEBDA（应用经济学与数据分析研究中心）
