Bayesian Fisher Information and Detection of a Small Change in a Parameter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.

Original languageEnglish (US)
Title of host publication2020 54th Annual Conference on Information Sciences and Systems, CISS 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728140841
DOIs
StatePublished - Mar 2020
Event54th Annual Conference on Information Sciences and Systems, CISS 2020 - Princeton, United States
Duration: Mar 18 2020Mar 20 2020

Publication series

Name2020 54th Annual Conference on Information Sciences and Systems, CISS 2020

Conference

Conference54th Annual Conference on Information Sciences and Systems, CISS 2020
CountryUnited States
CityPrinceton
Period3/18/203/20/20

Keywords

  • Fisher information
  • ROC analysis
  • Shannon information
  • information theory

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing
  • Information Systems and Management
  • Safety, Risk, Reliability and Quality
  • Artificial Intelligence

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  • Cite this

    Clarkson, E. (2020). Bayesian Fisher Information and Detection of a Small Change in a Parameter. In 2020 54th Annual Conference on Information Sciences and Systems, CISS 2020 [9086195] (2020 54th Annual Conference on Information Sciences and Systems, CISS 2020). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CISS48834.2020.1570625392