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

随着现代生物技术的迅速发展，世界正在见证成像和空间数据的爆炸式增长。这些丰富的信息为解决许多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，或者遗传变异如何影响大脑的问题。这就需要用严格的统计方法来理解它。神经影像学研究可能涉及描述大脑解剖、功能和连通性的大型数据集，而成像遗传学研究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。在这些领域中出现的统计问题的激励下，本研究将为神经成像数据的贝叶斯分析开发新的方法。提出的研究计划有几个目标。首先，我们将开发相关的技术成像和遗传数据，允许非线性分析。我们将允许使用神经网络对大脑的总结测量的遗传标记的非线性效应。第二个目标是开发一个软件工具箱，该工具箱将实现在使用某些模型分析fMRI、MEG和EEG数据时所做的假设进行审查的技术。这些诊断将帮助从业者了解用于实现它们的统计模型或算法何时可能基于无效的假设，并实现修正以改进结果统计推断。第三个目标是制定策略，将经验fMRI数据的分析与从计算机大脑模型生成的fMRI数据相结合。这样做的基本原理是，计算机模型包含基于其公式和输入的信息，这些信息可以添加到经验fMRI数据中的信息中，以改进整体分析。第四个目标将侧重于开发将纵向功能磁共振成像数据与遗传标记联系起来的方法，即在研究中，受试者在随访过程中反复进行功能磁共振成像扫描。这种方法将被扩展到包括大脑结构连接数据。总的来说，这项研究计划将推动贝叶斯方法的发展，用于分析神经影像学数据。它将为本科生和研究生提供贝叶斯统计、计算方法和神经成像数据分析方面的宝贵培训。

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.