Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks

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 publicationConference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1365-1369
Number of pages5
ISBN (Electronic)9780738131269
DOIs
StatePublished - Nov 1 2020
Event54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020 - Pacific Grove, United States
Duration: Nov 1 2020Nov 5 2020

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2020-November
ISSN (Print)1058-6393

Conference

Conference54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
Country/TerritoryUnited States
CityPacific Grove
Period11/1/2011/5/20

Keywords

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

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

Cite this