Student Seminars

Houssein Shenastagh
PhD student, Department of Statistics, University of Michigan

Optimal detection of abrupt changes in Gaussian processes: fixed and increasing domain analysis

We study the problem of minimax optimal detection of shift in mean (SIM) in a univariate temporal Gaussian processes. The asymptotic analysis of existing algorithms of SIM detection such as CUSUM mainly adopt a strong and unrealistic assumption about the underlying process (e.g., independent and identically distributed samples). Moreover, the majority of former studies on SIM detection in time series with dependent observations, are restricted to the increasing domain asymptotic framework, in which the smallest distance between sampling points is bounded away from zero. Motivated by the problem of change detection in piecewise locally stationary process and zone of abrupt changes detection in spatial processes, we analyze the problem of SIM detection of Gaussian processes, in fixed domain setting, in which observations gets denser in a bounded domain. To our knowledge, this is the first work on SIM detection in fixed domain framework. We show that despite the optimality of CUSUM in increasing domain, it exhibits a poor performance in fixed domain. We also propose a minimax optimal detection algorithm by using the exact or approximated generalized likelihood ratio test (GLRT). The analysis of the detection rate demonstrates a strong connection between detection rate and the smoothness of the covariance function of underlying process. Lastly, in accordance with the developed theory, the numerical studies verify that GLRT has far more superior performance than CUSUM in fixed domain scenario.

Student Seminar Archive

For questions regarding the Statistics Student Seminar or if you are interested in presenting, please contact Joonha Park(joonhap@umich.edu) or Jingshen Wang(jshwang@umich.edu).