TY - GEN
T1 - Invariance and the Bayesian approach to generalized coherence tests
AU - Howard, Stephen D.
AU - Sirianunpiboon, Songsri
AU - Cochran, Douglas
N1 - Funding Information:
This work was supported in part by the Defence Science and Technology Group, Australia, in part by the U.S. Air Force Office of Scientific Research under grant numbers FA9550-12-1-0225and FA9550-12-1-0418,and in part by the Australian-American Fulbright Commission.
Publisher Copyright:
© 2017 IEEE.
PY - 2018/4/10
Y1 - 2018/4/10
N2 - 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.
AB - 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.
KW - Invariance
KW - Maximal invariant
KW - Multiple-channel detection
KW - Wijsman's Theorem
UR - http://www.scopus.com/inward/record.url?scp=85050983887&partnerID=8YFLogxK
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U2 - 10.1109/ACSSC.2017.8335622
DO - 10.1109/ACSSC.2017.8335622
M3 - Conference contribution
AN - SCOPUS:85050983887
T3 - Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
SP - 1573
EP - 1577
BT - Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
A2 - Matthews, Michael B.
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Y2 - 29 October 2017 through 1 November 2017
ER -