Bayesian Solutions to Model Selection, Parameter Estimation, and Spectral Analysis

模型选择、参数估计和谱分析是统计信号处理的三个重要领域。本研究利用贝叶斯理论探讨了这些学科中一些尚未解决的难题。感兴趣的主题包括基于渐近假设的模型选择规则的推导及其在数组处理、时间序列分析中的秩确定和向量场分割问题中的应用；瞬态信号分析及阈值信号、双线性模型等高度非线性模型的参数估计非平稳信号的贝叶斯谱分析。这项工作主要由三个同等重要的组成部分组成。首先是对这些问题的理论研究，从而提高对各种信号模型和概念的理解。二是解决方案的实际应用，包括医学图像的自动分割和单通道膜片钳电流的处理。第三种是纯粹的教育。本课程将为学生讲解贝叶斯推理的通用性及其在解决各种信号处理问题上的适用性。

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.