Bayesian Analysis and Interfaces

当今大数据领域许多最具挑战性的问题涉及处理多重测试问题，包括微阵列和其他生物信息学分析、综合征监测、高通量筛选等。同时进行数千或数百万次测试时的挑战是开发能够检测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（在整个人群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，部分关注个性化医疗。计算机模型的发展对于理解复杂过程至关重要，就像理解计算机模型与数据和不确定性之间的接口一样，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。最近关注科学可重复性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，该项目还将研究将p值转换为更可解释的数量的可能性，例如零对备择假设的几率。贝叶斯多重测试方法的吸引力在于，即使面对高度依赖的数据或测试统计数据，它也是最适合检测的，同时施加强大的控制来防止错误的发现。其实现的障碍在于开发适当的先验概率结构和进行计算。虽然不确定性量化的许多方面将被调查，但该项目将特别侧重于对输出大量时空数据场的复杂计算机模型的仿真器（近似）的迫切需要的开发。寻找最优贝叶斯和最优频率程序一致的情况具有重大的基础和实际意义。这种新协议通常是通过发展新的条件频率论程序而产生的。这将在两种方法的背景下完成，即研究正确发现和错误发现的几率和多端点测试。这也将推广到更一般的模型不确定性问题，使用鲁棒贝叶斯分析。

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.