Model selection, parameter estimation, and spectral analysis are three important areas in statistical signal processing. This research explores some difficult and unresolved problems in these disciplines by exploiting Bayesian theory. Topics of interest include the derivation of model selection rules based on asymptotic assumptions and their applications to problems in array processing, rank determination in time series analysis, and segmentation of vector fields; analysis of transient signals and parameter estimation of highly nonlinear models such as threshold signal models and bilinear models; and, Bayesian spectral analysis of nonstationary signals. This effort primarily consists of three equally important components. The first is a theoretical investigation into these problems that leads to an improved understanding of various signal models and concepts. The second is the practical application of the solutions, which includes automatic segmentation of medical images and the processing of single channel patch clamp currents. The third is purely educational. Students are given a practical exposition into the versatility of Bayesian inference and its applicability for solving a wide range of signal processing problems.
