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On the Informativeness of Measurements in Shiryaev's Bayesian Quickest Change Detection

Systems and Control 2019-09-17 v2

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.

Keywords

Cite

@article{arxiv.1903.03283,
  title  = {On the Informativeness of Measurements in Shiryaev's Bayesian Quickest Change Detection},
  author = {Jason J. Ford and Jasmin James and Timothy L. Molloy},
  journal= {arXiv preprint arXiv:1903.03283},
  year   = {2019}
}