Bayes estimation of number of signals

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).