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BAYES ESTIMATION OF NUMBER OF SIGNALS

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N. K. BANSAL^{1} AND M. BHANDARY^{2}

^{1} *Department of Mathematics, Statistics and Computer Science, Marquette University,*

Milwaukee, WI 53233, U.S.A.

^{2} *Chesapeake Biological Laboratory, University of Maryland, P.O. Box 38,*

Solomons, MD 20688, U.S.A.
(Received October 31, 1988; revised February 9, 1990)

**Abstract.**
Bayes estimation of the number of signals,
*q*, based on a binomial prior distribution is studied. It is found that
the Bayes estimate depends on the eigenvalues of the sample covariance
matrix *S* for white-noise case and the eigenvalues of the matrix
*S*_{2}(*S*_{1} + *A*)^{-1} for the colored-noise case, where
*S*_{1} is the sample covariance matrix of observations consisting only
noise, *S*_{2} the sample covariance matrix of observations
consisting both noise and signals and *A* is some positive definite
matrix. Posterior distributions for both the cases are derived by
expanding zonal polynomial in terms of monomial symmetric functions and
using some of the important formulae of James (1964, *Ann. Math.
Statist.*, **35**, 475-501).

*Key words and phrases*:
Zonal polynomial, white-noise,
colored-noise, Haar measure, partitions.

**Source**
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