L. Dou et Rjw. Hodgson, BAYESIAN-INFERENCE AND GIBBS SAMPLING IN SPECTRAL-ANALYSIS AND PARAMETER-ESTIMATION .1., Inverse problems, 11(5), 1995, pp. 1069-1085
Bayesian inference theory and Gibbs sampling techniques are introduced
and applied to spectral analysis and parameter estimation for both si
ngle- and multiple-frequency signals. Specifically, the marginal poste
rior probabilities for amplitudes and frequencies are obtained by usin
g Gibbs sampling without performing the integrations, no mater whether
the variance of the noise is known or unknown. The best estimates of
the parameters can be inferred from these probabilities together with
the corresponding variances. In addition, when the variance of the noi
se is unknown, and estimate about the variance of the noise can also b
e made. Comparisons of our results have been made with results using t
he FFT method as well as with Bretthorst's method. The approach outlin
ed shows several advantages.