Uncertainty-Aware Quickest Change Detection: An Experimental Study

James Zachary Hare, Lance M. Kaplan

Abstract: In this work, we study the problem of Quickest Change Detection which aims to detect when a stream of observations transitions from being drawn from a pre-change distribution to a post-change distribution as quickly as possible. Traditionally, either information is completely known about the distributions, or no information is known and their parameters are estimated using frequentist approaches, e.g., Generalized Likelihood Ratio test. Recently, the Uncertain Likelihood Ratio (ULR) test was proposed for the QCD problem which relaxes both of these assumptions to form a Bayesian test that allows for no knowledge, partial knowledge, and full knowledge of the parameters of the distributions. In this work, we extend the ULR test to improve the order of operations required to compute the test statistic using a windowing method to form the Windowed Uncertain Likelihood Ratio (W-ULR) algorithm. We then applied it to multivariate Gaussian observations and empirically evaluated the average detection delay and missed detections for various false alarm rates under various operating conditions. The results show that the W-ULR outperforms the (windowed) GLR test, which is consistent with the initial findings.