Some Bayesian considerations in spectral estimation

SUMMARY This paper considers the problem of incorporating prior information about the shape and smoothness of a spectral density into the formation of a spectral estimate. Two types of finite dimensional parameters are considered, the spectral ordinates at a specified collection of frequencies and the amount of power in each of a set of frequency bands. A method which is conditional on the asymptotic distribution of periodogram averages is proposed. A formal procedure applies Bayes's theorem. A conjugate prior distribution is a product of inverted gamma distributions. The results extend to estimation of a spectral density matrix in the vector case.