Invariance and the Bayesian approach to generalized coherence tests

Stephen D. Howard, Songsri Sirianunpiboon, Douglas Cochran

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

Abstract

This paper considers the problem of testing for mutual independence of multiple sets of complex Gaussian vectors. This problem has classical roots in statistics and has been of recent interest in the signal processing literature in connection with multi-channel signal detection. The probability distribution of the maximal invariants under the action of a subgroup of the full invariance group of the problem is derived for both hypotheses. It is shown that for parameter space, the maximal invariants under the action of this subgroup form a compact space on which proper non-informative prior distributions can be constructed. Bayesian likelihood ratios for the maximal invariants are derived for various proper prior distributions. Previously, Bayesian likelihood ratios associated with non-informative prior distributions for this problem could only be constructed through considerably less satisfactory limiting techniques.

Original languageEnglish (US)
Title of host publicationConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
EditorsMichael B. Matthews
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1573-1577
Number of pages5
Volume2017-October
ISBN (Electronic)9781538618233
DOIs
StatePublished - Apr 10 2018
Event51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 - Pacific Grove, United States
Duration: Oct 29 2017Nov 1 2017

Other

Other51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
CountryUnited States
CityPacific Grove
Period10/29/1711/1/17

Keywords

  • Invariance
  • Maximal invariant
  • Multiple-channel detection
  • Wijsman's Theorem

ASJC Scopus subject areas

  • Control and Optimization
  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Biomedical Engineering
  • Instrumentation

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  • Cite this

    Howard, S. D., Sirianunpiboon, S., & Cochran, D. (2018). Invariance and the Bayesian approach to generalized coherence tests. In M. B. Matthews (Ed.), Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 (Vol. 2017-October, pp. 1573-1577). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACSSC.2017.8335622