Mathematical Sciences: Sampling Based Methods for Bayesian Computation

数学科学：基于采样的贝叶斯计算方法

• 批准号: 8918563
• 负责人: Alan Gelfand
• 金额: $ 5.94万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8918563&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Sampling; Based; Methods

The calculation of marginal posterior densities is an essential component of the application of Bayesian inference to data. This research involves the use of the method of Gibbs sampling in the computation of these densities when they are represented as integrals over spaces of extremely high dimension. Theoretical issues addressed include the extension of the "ratio of uniforms" method of sampling to multivariate distributions as well as accurate calculations of expectations. The development of satisfactory convergence criteria will also be attacked. In particular, a formal methodology that yields an automated decision will be sought.

边际后验密度的计算是将贝叶斯推理应用于数据的重要组成部分。 这项研究涉及在计算这些密度时使用吉布斯采样方法，当它们表示为极高维空间上的积分时。 解决的理论问题包括将“均匀比率”抽样方法扩展到多元分布以及准确计算期望。令人满意的收敛标准的制定也将受到攻击。 特别是，将寻求一种能够产生自动决策的正式方法。