Biostatistics for Spatial and High-Dimensional Data: New Statistical Methods for Neuroimaging and Imaging Genomics

随着现代生物技术的快速发展，世界正在见证数据的爆炸式增长。这些丰富的信息为解决许多最基本的科学问题提供了丰富的资源，例如，关于大脑如何工作的问题，或者关于基因变异如何影响大脑的问题。尽管如此，科学界面临的一个主要挑战是现代数据集的庞大规模和复杂性，这迫切需要严格的统计方法来处理和理解它。特别是，神经影像学研究可以涉及描述大脑解剖、功能和连通性的大型和非常详细的数据集；成像基因组学这一新兴领域的研究，其兴趣在于发现与大脑结构和功能相关的遗传变异，涉及对大脑图像和高通量基因分型产生的额外数据的综合分析。在后一种情况下，在全脑全基因组研究中进行超过10亿次的关联统计测试并不罕见。在这些领域中出现的具有挑战性的统计问题的激励下，本文提出的研究将为未知参数数量大于样本量的高维环境中的空间和时空统计分析开发新的方法。

With the rapid advancement of modern biotechnology, the world is witnessing an explosion of data. This wealth of information represents an abundant resource for tackling many of the most fundamental scientific questions, for example, questions about how the brain works, or questions about how genetic variation influences the brain. Despite this, a major challenge facing the scientific community is the sheer size and complexity of modern datasets which has created a pressing need for rigorous statistical approaches in order to process and understand it. In particular, neuroimaging studies can involve large and exquisitely detailed datasets describing the anatomy, function, and connectivity of the brain; while studies in the nascent field of imaging genomics, where interest lies in discovering the genetic variants associated with the structure and function of the brain, involves a combined analysis of both brain images as well as additional data arising from high-throughput genotyping. In the latter setting, it is not unusual to conduct well over one billion statistical tests of association in a brain-wide genome-wide study. Motivated by the challenging statistical problems arising in these areas, the research proposed here will develop new methodology for spatial and spatiotemporal statistical analysis in high-dimensional settings where the number of unknown parameters is larger than the sample size. Increasingly, state-of-the-art neuroimaging studies collect data using multiple modalities. Such studies are well-motivated by the fact that different imaging techniques such as magnetoencephalography (MEG), electroencephalography (EEG), and functional magnetic resonance imaging (fMRI) provide complimentary sources of information, and their union provides a more complete picture describing the function of the brain. Developing rigorous approaches to analyzing such data within a unified framework is made difficult by the size of the data, the number of unknown parameters of interest, and the differing spatial and temporal scales associated with each modality. Building upon recent work focussing on spatial statistics for neuroimaging data analysis, the primary objective of the research proposed here is the development of novel, useful, and computationally tractable methods and software for the analysis of complex data arising in neuroimaging and imaging genomics. Specific research goals are as follows: (1) To develop approaches for electromagnetic brain mapping based on the combined analysis of magnetoencephalography (MEG), electroencephalography (EEG), and functional magnetic resonance imaging (fMRI) data. (2) To harness recent developments in nonlinear dimension reduction for extracting information and solving classification problems involving MEG/EEG data. (3) To develop new statistical models for analysis in studies of imaging genomics that effectively exploit the spatial structure of the brain imaging data when examining an extremely large number of genetic associations. The anticipated outcomes of the research program are the development of new statistical tools that will allow researchers to better combine and analyze information from different sources, from multiple imaging modalities; from brain imaging and high-throughput genotyping; and new classification methods that can be applied to the decoding of mental states as well as to the development of imaging biomarkers of neurological disorders.