Bayes and Empirical Bayes Model Selection

贝叶斯和经验贝叶斯模型选择

• 批准号: 9803756
• 负责人: Edward George
• 金额: $ 8.72万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803756&HistoricalAwards=false
• 关键词: Bayes; Empirical; Model; Selection

----------------------------------------------------------------------- Proposal Number: DMS 9803756 PI: Edward I. George Institution: University of Texas Project: Bayes and Empirical Bayes Model Selection Abstract: Bayes and empirical Bayes approaches for model selection are studied, developed and enhanced for a variety of different settings. First of all, theoretical frequentist risk properties of recently discovered empirical Bayes selection criteria are established for the canonical linear model setting. For graphical model selection, connections between frequentist and Bayesian methods are investigated and used to motivate new empirical Bayes methods. For wavelet representations, robust empirical Bayes selection procedures are developed which accommodate heavy tailed noise distributions. For Bayesian CART modeling, new families of structured hierarchical priors are developed. To facilitate and enhance model search, new MCMC algorithms are developed which move across sets of models rather than single models. These algorithms use new transition kernel steps, such as transplantation, which can rapidly traverse the kinds of multimodal model posterior distributions that arise in this context. These algorithms also incorporate stochastic heating and cooling to further increase movement. This research ultimately concerns the development of statistical methods for discovering systematic structure in large multi-variable data sets. This general problem is of substantial importance because of the explosive growth in the technology to collect and analyze such data. Indeed, such large data sets occur naturally in federal strategic areas of national concern including telecommunications, biotechnology, and climatology. A standard statistical approach in such settings is to search for "promising" statistical models within some prespecified, large, flexible class of potential models. Once found, the challenge is to estimate the mod el and draw meaningful inference. These tasks can be especially difficult when the class of potential models is huge, as is typically the case the number of variables is large. The main thrust of this work will be to develop new methods to confront these challenges and broaden the scope of the statistical approach.

----------------------------------------------------------------------- Proposal Number: DMS 9803756 PI: Edward I. George Institution: University of Texas Project: Bayes and Empirical Bayes Model Selection Abstract: Bayes and empirical Bayes approaches for model selection are studied, developed and enhanced for a variety of different settings. 首先，针对规范线性模型设置建立了最近发现的经验贝叶斯选择标准的理论频繁风险特性。 对于图形模型选择，研究了常见主义者和贝叶斯方法之间的连接，并用于激励新的经验贝叶斯方法。 对于小波表示，开发了强大的经验贝叶斯选择程序，可容纳重型尾噪声分布。 对于贝叶斯购物车建模，开发了结构性分层先验的新家庭。 为了促进和增强模型搜索，开发了新的MCMC算法，这些算法跨越了模型集，而不是单个模型。 这些算法使用新的过渡内核步骤，例如移植，它们可以迅速遍历在这种情况下出现的多模型后验分布。 这些算法还结合了随机加热和冷却，以进一步增加运动。 这项研究最终涉及在大型多变量数据集中发现系统结构的统计方法的发展。由于收集和分析此类数据的技术爆炸性增长，因此这个总体问题非常重要。 确实，如此大的数据集自然发生在国家关注的联邦战略领域，包括电信，生物技术和气候学。 在这种情况下，一种标准的统计方法是在某些预先指定的，大型，灵活的潜在模型类别中搜索“有希望的”统计模型。 一旦发现，挑战是估计Mod El并提取有意义的推断。 当潜在模型类巨大时，这些任务可能特别困难，而变量的数量通常很大。 这项工作的主要目的是开发面对这些挑战并扩大统计方法范围的新方法。