Collaborative Research: Bayesian Analysis and Applications

合作研究：贝叶斯分析与应用

• 批准号: 1007773
• 负责人: James Berger
• 金额: $ 33.3万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007773&HistoricalAwards=false
• 关键词: Collaborative; Research; Bayesian; Analysis; Applications

Five research areas in Bayesian analysis, involving theory, methodology and application, will be pursued: objective Bayesian analysis, multiplicity adjustment, search and approximations in model selection, analysis of complex computer models, and differences between Bayes and empirical Bayes analysis. Research in objective Bayesian analysis will focus on the development of objective priors, together with their computational implementation, in semi-invariant contexts, which include spatial problems and problems arising in psychiatry. The Bayesian approach to multiplicity correction has the attraction that it does not depend on the error structure of the data; multiplicity correction is done only through the prior probabilities assigned to models or other multiplicity features. Understanding which probability assignments do, and do not, adjust for multiplicity will be an important feature of this research. A focus of the research on model selection will be the development of a generalization of BIC which is much more widely applicable than the standard version, especially overcoming the major hurdle of defining effective sample size for a parameter. Advances in these areas will have application to research involving the analysis and use of complex computer models of processes. Also, surprising differences between Bayes and empirical Bayes analysis arise in several of the above settings, and better understanding of these differences will also be a focus of the research.Objective Bayesian analysis has existed for over 250 years, but interest in the field has increased markedly in recent years. A major reason is that many of the significant scientific problems today (such as much of climate change research) involve some type of assimilation of data and physical modeling, typically done by Bayesian methods. Many of today?s most challenging problems ? including microarray and other bioinformatic analyses, syndromic surveillance, high-throughput screening, and many others ? involve consideration of multiple-testing with a huge number of possible tests, and require major multiplicity adjustments. For instance, the work on multiplicity will be done in the context of subgroup analysis in clinical trials, providing major new insights into HIV vaccine trials, and in refining detection methodology in high-energy physics.

贝叶斯分析的五个研究领域，涉及理论，方法和应用，将追求：客观贝叶斯分析，多重调整，搜索和近似模型选择，复杂的计算机模型分析，贝叶斯和经验贝叶斯分析之间的差异。在客观贝叶斯分析的研究将集中在客观先验的发展，连同他们的计算实现，在半不变的情况下，其中包括空间问题和精神病学中出现的问题。贝叶斯方法的多重性校正具有的吸引力，它不依赖于数据的错误结构;多重性校正只通过分配给模型或其他多重性特征的先验概率进行。了解哪些概率分配做，不，调整多重性将是本研究的一个重要特点。模型选择研究的一个重点将是BIC的推广，这是更广泛的适用于比标准版本的发展，特别是克服了定义有效样本量的参数的主要障碍。这些领域的进展将应用于涉及分析和使用复杂计算机模型的研究。此外，贝叶斯和经验贝叶斯分析之间的惊人差异出现在上述几个设置，更好地了解这些差异也将是研究的重点。客观贝叶斯分析已经存在了250多年，但在该领域的兴趣显着增加，近年来。一个主要原因是，今天许多重要的科学问题（如气候变化研究）涉及某种类型的数据同化和物理建模，通常由贝叶斯方法完成。今天很多人？最具挑战性的问题是什么？包括微阵列和其他生物信息学分析，症状监测，高通量筛选，以及许多其他？涉及考虑具有大量可能测试的多重测试，并且需要重大的多重性调整。例如，关于多重性的工作将在临床试验亚组分析的背景下进行，为艾滋病毒疫苗试验提供重要的新见解，并改进高能物理学的检测方法。