Biostatistics for Spatial and High-Dimensional Data: Bayesian Methods for Image Analysis

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With the rapid advancement of modern biotechnology, the world is witnessing an explosion of imaging and spatial data. This wealth of information represents an abundant resource for tackling many scientific questions, for example, questions about how the brain works, or how genetic variation influences the brain. This has created a need for rigorous statistical approaches to understand it. Neuroimaging studies can involve large datasets describing the anatomy, function, and connectivity of the brain, while studies in imaging genetics involve a combined analysis of brain images and additional data arising from high-throughput genotyping. Motivated by the statistical problems arising in these areas, this research will develop new methodology for the Bayesian analysis of neuroimaging data. The are several objectives of the proposed research program. First, we will develop techniques for relating imaging and genetic data that allow for nonlinear analysis. We will allow for nonlinear effects of genetic markers on summary measures of the brain using neural networks. A second objective is the development of a software toolbox that will implement techniques for scrutinizing the assumptions made when using certain models for the analysis of fMRI, MEG and EEG data. These diagnostics will help practitioners understand when statistical models or the algorithms used to implement them might be based on assumptions that are not valid, and implement corrections to improve the resulting statistical inference.  A third objective will develop strategies for combining the analysis of empirical fMRI data with fMRI data that are generated from a computer model of the brain. The rationale for this is that the computer model contains information based on its formulation and inputs that can be added to the information in the empirical fMRI data to improve the overall analysis. The fourth objective will focus on developing methods to relate longitudinal fMRI data, that is in studies where subjects have an fMRI scan repeatedly during the course of follow-up, to genetic markers. This methodology will then be extended to include structural brain connectivity data. Overall, this research program will advance the development of Bayesian methods for the analysis of neuroimaging data. It will provide valuable training to undergraduate and graduate students in Bayesian statistics, computational methods and the analysis of neuroimaging data.