On the informativeness of measurements in Shiryaev's Bayesian quickest change detection. (January 2020)

• Record Type: Journal Article
• Authors: Ford, Jason J.; James, Jasmin; Molloy, Timothy L.
• Is Part Of: Automatica. Volume 111(2020)
• Publication Date: 2020-01
• Subjects: Bayesian quickest change detection -- Detection algorithms -- Markov models -- Super-martingale -- Maximal inequality; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108645
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper provides the first description of a weak practical super-martingale phenomenon that can emerge in the test statistic in Shiryaev's Bayesian quickest change detection (QCD) problem. We establish that this super-martingale phenomenon can emerge under a condition on the relative entropy between pre and post change densities when the measurements are insufficiently informative to overcome the change time's geometric prior. We illustrate this super-martingale phenomenon in a simple Bayesian QCD problem which highlights the unsuitability of Shiryaev's test statistic for detecting subtle change events.