Some Bayesian considerations in spectral estimation

This paper considers the problem of incorporating prior information about the shape and smoothness of a specrtal 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 amoun...

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Bibliographic Details
Published in:Biometrika 1977-04, Vol.64 (1), p.79-84
Main Author: Shaman, Paul
Format: Article
Language:English
Subjects:
Data smoothing
Density estimation
Estimation methods
Frequency band
Inverted gamma distribution
Mathematics
Periodogram
Prior distribution
Prior learning
Signal bandwidth
Smoothing
Spectral density
Spectral energy distribution
Time series
Vibrational frequencies
Weighting functions
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Summary:This paper considers the problem of incorporating prior information about the shape and smoothness of a specrtal 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/64.1.79