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

模型选择、参数估计和谱分析的贝叶斯解决方案

• 批准号: 9506743
• 负责人: Petar Djuric
• 金额: $ 17.63万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9506743&HistoricalAwards=false
• 关键词: Bayesian; Solutions; Model; Selection; Parameter

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.

模型选择、参数估计和谱分析是统计信号处理中的三个重要领域。 本研究利用贝叶斯理论探讨了这些学科中一些困难和尚未解决的问题。 感兴趣的主题包括推导模型选择规则的基础上渐近假设及其应用的问题，在阵列处理，在时间序列分析中的秩确定，并分割向量场;瞬态信号的分析和高度非线性模型，如阈值信号模型和双线性模型的参数估计;和，贝叶斯谱分析的非平稳信号。 这项工作主要包括三个同等重要的组成部分。 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。 第三是纯粹的教育。 学生将实际阐述贝叶斯推理的多功能性及其在解决各种信号处理问题中的适用性。