Collaborative Research: Bayesian Analysis and Applications

贝叶斯分析的五个研究领域，包括理论、方法论和应用：客观贝叶斯分析、多样性调整、模型选择中的搜索和近似、复杂计算机模型的分析以及贝叶斯分析和经验贝叶斯分析的差异。客观贝叶斯分析的研究将集中于在半不变环境中发展客观先验及其计算实现，其中包括空间问题和精神病学中出现的问题。多重性校正的贝叶斯方法的吸引力在于它不依赖于数据的错误结构；多重性校正仅通过分配给模型或其他多重性特征的先验概率来完成。了解哪些概率分配可以调整，哪些不调整，这将是这项研究的一个重要特点。模型选择的一个研究重点将是发展比标准版本更广泛的BIC的推广，特别是克服为参数确定有效样本量的主要障碍。这些领域的进展将应用于涉及分析和使用复杂计算机过程模型的研究。此外，在上述几种情况下，贝叶斯分析和经验贝叶斯分析之间出现了惊人的差异，更好地理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，但近年来对该领域的兴趣显著增加。一个主要原因是，今天的许多重大科学问题(如许多气候变化研究)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。今天有多少？S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、综合征监测、高通量筛查和许多其他？涉及到对大量可能测试的多重测试的考虑，并需要进行重大的多样性调整。例如，关于多样性的工作将在临床试验的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，并改进高能物理中的检测方法。

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.