The Bayesian statistical inference theory is studied and applied to two problems in applied physics: spectral analysis and parameter estimation in time series data and hyperfine parameter extraction in Mossbauer spectroscopy. The applications to spectral analysis and parameter estimation for both single- and multiple-frequency signals are presented in detail. Specifically, the marginal posterior probabilities for the amplitudes and frequencies of the signals are obtained by using Gibbs sampling without performing the integration, no matter 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. When the variance of the noise is unknown, an estimate about the variance of the noise can also be made. Comparisons of our results have been made with results using the Fast Fourier Transformation (FFT) method as well as Bretthorst's method. The same numerical approach is applied to some complicated models and conditions, such as periodic but non-harmonic signals, signals with decay, and signals with chirp. Results demonstrate that even under these complicated conditions the Bayesian inference and Gibbs sampling can still give very accurate results with respect to the true result. Also through the use of the Bayesian inference methods it is possible to choose the most probable model based on known prior information of data, assuming a model space. The Bayesian inference theory is applied to hyperfine parameter extraction in Mossbauer spectroscopy for the first time. The method is a free-form model extraction approach and gives full error analysis of hyperfine parameter distributions. Two applications to quadrupole splitting distribution analysis in Fe-57 Mossbauer spectroscopy are presented. One involves a single site of Fe3+ and the other involves two sites for Fe3+ and Fe2+. In each case the method gives a unique solution to the distributions with arbitrary shape and is not sensitive to the elemental doublet parameters. The Bayesian inference theory is also applied to the hyperfine field distribution extraction. Because of the complexity of the elemental lineshape, all the other extraction methods can only use the first order perturbation sextet as the lineshape function. We use Blaes' exact lineshape model to extract the hyperfine field distribution. This is possible because the Bayesian inference theory is a free-form model extraction method. By using Blaes' lineshape function, different cases of orientations between the electric field gradient principle axis directions and the magnetic hyperfine field can be studied without making any approximations. As an example the ground state hyperfine field distribution of Fe65Ni35 Invar is extensively studied by using the method. Some very interesting features of the hyperfine field distribution are identified.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/8483 |
| Date | January 1999 |
| Creators | Dou, Lixin. |
| Contributors | Hodgson, R., |
| Publisher | University of Ottawa (Canada) |
| Source Sets | Université d’Ottawa |
| Detected Language | English |
| Type | Thesis |
| Format | 175 p. |
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