CAREER: Bringing richly structured Bayesian models into the discrete-data realm via new data-augmentation theory and algorithms

现代贝叶斯工具箱包含许多为连续数据量身定做的高度结构化模型。这些工具允许我们处理不仅大，而且密集的数据集：在时间或空间上变化的，丰富的协变量，或具有层次结构的深层，并以更巴洛克的方式进行索引。但在对离散数据进行建模方面，该领域的进展还远远不够。事实上，许多常见的离散数据模型长期以来一直被认为太难在常规基础上使用，这是因为出现的可能性函数在分析上不方便。研究人员将开发用于离散数据问题的推理工具，这些工具利用新的数据扩充方案以及并行和分布式计算的最新进展。离散数据集通常涉及事件计数或分类结果(是或否，这个或那个选择)。研究人员的研究目标是利用详细的空间信息来更好地模拟和预测这些结果。在许多情况下，这将涉及到物理空间。例如，当公共卫生当局在一群医院寻找过多的呼吸道感染报告时，或者当执法人员在拥挤的公共活动中部署检测辐射异常的设备时，空间模式非常重要。但它也可能涉及到一个更抽象的空间概念。例如，临床试验中的患者可以位于由他们的基因和行为定义的空间中。这些信息对个性化医学很有用：即，即使更广泛的人群不属于药物帮助的特殊亚群，也能确定某人是否属于这个特殊的亚群。虽然拟议的研究属于统计学方法论领域，但这项工作本质上是跨学科的，并寻求为紧迫的科学问题提供统计解决方案。国际统计协会有非常好的想法，如何以更跨学科和更面向数据的方式转变统计教育，使德克萨斯大学奥斯汀分校能够像国际统计协会所写的那样，成为“世界上最具创新性的统计项目之一”。他的研究被整合到德克萨斯大学奥斯汀分校新成立的统计和科学计算部门(SSC)的教育中。

The modern Bayesian toolbox contains many highly structured models tailored for continuous data. These tools allow us to handle data sets that are not merely large, but also dense: varying in time or space, rich with covariates, or deeply layered with hierarchical structure, and indexed in ever more baroque ways. But the field has not progressed nearly as far in modeling discrete data. Indeed, many common discrete-data models have long been viewed as too difficult to work with on a routine basis, due to the analytically inconvenient form of the likelihood functions that arise. The investigator will develop inferential tools for discrete-data problems that exploit new data-augmentation schemes as well as recent advances in parallel and distributed computing.Discrete data sets typically involve either event-count or categorical outcomes (yes or no, this choice or that). The goal of the investigator's research is to leverage detailed spatial information to better model and predict these outcomes. In many cases this will involve physical space. For example, spatial patterns are very important when public health authorities look for excess reports of respiratory infection at a cluster of hospitals, or when law-enforcement officers deploy equipment that detects radiation anomalies at a crowded public event. But it may also involve a more abstract notion of space. For example, patients in a clinical trial can be located in a space defined by their genes and behavior. This information is useful for personalized medicine: that is, deciding whether someone belongs to a special sub-group that is helped by a drug, even if the wider population isn't. Though the proposed research is in the area of statistical methodology, the work is inherently interdisciplinary, and seeks to provide statistical solutions for pressing scientific problems. The PI has very good ideas how to transform the education of statistics in a more interdisciplinary and more data oriented way so that UT-Austin can become "one of the most innovative statistics programs in the world" as the PI writes. His research is integrated into the education of the new Division of Statistics and Scientific Computation (SSC) at UT-Austin.