Bayes estimation of number of signals. (English) Zbl 0761.62030
Summary: 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 the 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 of noise, \(S_ 2\) the sample covariance matrix of observations consisting both of noise and signals and \(A\) is some positive definite matrix. Posterior distributions for both the cases are derived by expanding zonal polynomials in terms of monomial symmetric functions and using some of the important formulae of A. T. James [Ann. Math. Statist. 35, 475-501 (1964; Zbl 0121.366)].
MSC:
| 62F15 | Bayesian inference |
| 62N99 | Survival analysis and censored data |
| 62M99 | Inference from stochastic processes |
| 62P99 | Applications of statistics |
Keywords:
Haar measure; partitions; signal processing; Bayes estimation; number of signals; binomial prior distribution; eigenvalues; sample covariance matrix; white-noise case; colored-noise case; Posterior distributions; zonal polynomials; monomial symmetric functionsCitations:
Zbl 0121.366References:
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