Bayesian Analysis and Interfaces

当今大数据领域最具挑战性的许多问题涉及处理多个测试的问题，包括微阵列和其他生物信息学分析、综合征监测、高通量筛查等许多问题。当同时进行数千或数百万次测试时，面临的挑战是开发能够检测到真实信号但防止错误发现的测试方法。这项研究的关键背景包括亚组分析(在整个人口的亚组中寻找治疗效果)和多终点分析(同时寻找不同的治疗效果)，在与制药行业的接口中，部分侧重于个性化药物。计算机模型的开发对于理解复杂的过程至关重要，就像理解计算机模型与数据和不确定性的接口一样，这通常被称为不确定性量化。不确定性量化研究的直接科学应用将是地球物理灾害概率的预测和风场模型。最近对科学重现性的担忧的两个最重要的原因是未能控制多样性和对p值的普遍误解。除了前面提到的多重性控制之外，该项目还将调查将p值转换为更可解释的数量的可能性，例如零值对替代假设的赔率。多项测试的贝叶斯方法的吸引力在于，即使面对高度依赖的数据或测试统计数据，它也具有最佳的检测能力，同时实施强大的控制以防止错误发现。其实施的障碍在于开发适当的先验概率结构和进行计算。虽然将调查不确定性量化的许多方面，但该项目将特别关注迫切需要的仿真器(近似)的开发，以用于产生大量时空数据场的复杂计算机模型。找到最优贝叶斯和最优频率法一致的情况有很大的好处，既有基础的，也有实用的。这类新协议通常是通过开发新的有条件频率程序而产生的。这将在两种方法的背景下进行，即研究正确到错误发现的几率和多端点测试。这也将被推广到更一般的模型不确定性问题，使用稳健的贝叶斯分析。

Many of today's most challenging problems in Big Data involve dealing with the problem of multiple testing, including microarray and other bioinformatic analyses, syndromic surveillance, high-throughput screening, and many others. The challenge when simultaneously conducting thousands or millions of tests is to develop testing methodology that can detect true signals but prevent false discoveries. Crucial contexts for this research include subgroup analysis (searching for a treatment effect in subgroups of the entire population) and multiple endpoint analysis (simultaneously looking for different treatment effects), in interfaces with the pharmaceutical industry and with partial focus on personalized medicine. Development of computer models is crucial in understanding complex processes, as is understanding the interfaces of the computer models with data and uncertainty, often named Uncertainty Quantification. The immediate science applications of the research on Uncertainty Quantification will be to prediction of geophysical hazard probabilities and to models of wind fields. Two of the most significant reasons for the recent concern over reproducibility of science are the failure to control for multiplicities and the common misinterpretation of p-values. In addition to the earlier mentioned multiplicity control, the project will investigate the possibility of converting p-values to more interpretable quantities, such as the odds of the null to the alternative hypothesis. The Bayesian approach to multiple testing has the attraction that it is optimally powered for detection, even in the face of highly dependent data or tests statistics, while exerting strong control to prevent false discoveries. The barriers to its implementation are in developing the appropriate prior probability structures and carrying out the computation. While numerous aspects of Uncertainty Quantification will be investigated, the project will particularly focus on the crucially needed development of emulators (approximations) to complex computer models which output massive space-time data fields. Finding situations in which optimal Bayesian and optimal frequentist procedures agree has major benefits, both foundational and practical. Such new agreements typically arise through development of new conditional frequentist procedures. This will be done in the context of two methodologies, study of the odds of correct to false discovery and multiple endpoint testing. This will also be generalized to more general model uncertainty problems, using robust Bayesian analysis.