Bayesian inference and Gibbs sampling in spectral analysis and parameter estimation: II

Abstract

Based on the theory of Bayesian inference and Gibbs sampling presented in part I of this series, the same numerical approach is applied to some more complicated models and conditions, such as periodic but non-harmonic signals, signals with decay, and signals with chirp, in spectral analysis and parameter estimation. Results demonstrate that even under these complicated conditions Bayesian inference and Gibbs sampling can still give very accurate results. It is also demonstrated that through the use of Bayesian inference methods it is possible to choose the most probable model based on known prior information and data, assuming a model space. Two model selection examples are presented which demonstrated the reliability of this approach.