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.

- 建议编号：DMS 9803756 PI： 爱德华岛乔治机构： 德克萨斯大学 项目名称： 贝叶斯和经验贝叶斯模型选择 摘要： 研究了贝叶斯和经验贝叶斯模型选择方法， 为各种不同的设置开发和增强。 首先，在典型线性模型下，建立了最近发现的经验贝叶斯选择准则的理论频率论风险性质。 对于图形模型选择，频率论和贝叶斯方法之间的连接进行了研究，并用于激励新的经验贝叶斯方法。 对于小波表示，强大的经验贝叶斯选择程序的开发，以适应重尾噪声分布。 贝叶斯CART建模，新的家庭结构化的层次先验的开发。 为了促进和增强模型搜索，开发了新的MCMC算法，该算法跨模型集而不是单个模型移动。 这些算法采用了移植等新的转换核步骤，能够快速地遍历各种多模态 模型后验分布出现在这种情况下。 这些算法还结合了随机加热和冷却，以进一步增加运动。 这项研究最终涉及的统计方法的发展，发现系统的结构，在大型多变量数据集。由于收集和分析这些数据的技术的爆炸性增长，这个一般问题具有实质性的重要性。 事实上，如此庞大的数据集自然出现在联邦国家关注的战略领域，包括电信、生物技术和气候学。 在这种情况下，一个标准的统计方法是在一些预先指定的、大的、灵活的潜在模型类别中搜索“有希望的”统计模型。 一旦找到，挑战是估计模型并得出有意义的推论。 当潜在模型的类别很大时，这些任务可能特别困难，因为通常情况下变量的数量很大。 这项工作的主旨将是制定新的方法来应对这些挑战，并扩大 统计方法。