Analysis of the weighted Shiryaev-Roberts procedure in the problem of changepoint detection for models with unknown post change parameters

A problem of detecting a change in the properties of a random process (disorder) with unknown post change parameters is considered. In this problem, two models of an observable random process are considered: a Gaussian process and an autoregressive process of the first order. In this paper, we propose a changepoint detection algorithm for models with unknown post change parameters, viz. the weighted Shiryaev-Roberts procedure. This approach makes it possible to effectively solve many problems encountered in practice when the properties of a random process after the changepoint are not fully known. Analysis of detection characteristics for the weighted Shiryaev-Roberts procedure is carried out and compared with the detection characteristics of the Shiryaev-Roberts procedure, when the post changes of the parameters of the random process are known. The results show that the use of the weighted Shiryaev-Roberts procedure allows for detecting the changepoint with a given level of false detections, while not losing significantly to the characteristics of the Shiryaev-Roberts procedure, when the parameters of the random process after the changepoint are known.