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.
