BAYESIAN-INFERENCE AND GIBBS SAMPLING IN SPECTRAL-ANALYSIS AND PARAMETER-ESTIMATION .1.

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.