Random fields and geometry with applications to brain imaging

随机场和几何在脑成像中的应用

• 批准号: 349817-2007
• 负责人: Taylor, Jonathan
• 金额: $ 2.91万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Accelerator Supplements
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=365219
• 关键词: Random; fields; geometry; applications; brain

The objective of this research is to develop theoretical and applied statistical methods for the analysis of / signal detection in brain mapping data, specifically those methods related to random fields.The statistical challenge is to develop methods for simultaneous inference to address the problem of detecting significant activation in these images. I have studied this using geometric tools originally developed by Robert Adler twenty years ago, and more recently by Keith Worsley. My work in this area has resulted in (i) a geometric tool known as the Gaussian Kinematic Formula that has unified and simplified much of the existing literature on random fields and (ii) the strongest known results for the accuracy of the approximation in a general setting. I propose to use these tools to study new non-Gaussian models of random fields arising from saddle-point type approximations as well as stable random fields. I also propose to study the behaviour of these approximations in high dimensions and their relations with large random matrices. These results will have applications in the study of non-Gaussian brain imaging data, as well as high-dimensional inference.An alternative approach to this problem is to use empirical Bayes techniques often referred to as False Discovery Rate (FDR) techniques. My work in this area has focused on asymptotic control of the FDR as well as useful summary statistics of FDR: the miss rate, and tail strength of a collection of p-values. In this proposal, I propose to extend the work of Genovese and Wasserman on FDR for random fields by modifying the simultaneous inference problem to one which recognizes the spatial structure inherent in brain imaging data.For any advances in statistical methodology addressing the simultaneous inference problem to be of use to the brain imaging community, they must be integrated into the researcher's software environment. All statistical techniques described in this proposal will be integrated into NiPy, a multi-center neuroimaging software project, of which I am one of the principal developers.

这项研究的目标是发展理论和应用的统计方法来分析脑图数据中的信号检测，特别是那些与随机领域相关的方法。统计学上的挑战是开发用于同时推理的方法来解决在这些图像中检测显著激活的问题。我用20年前由罗伯特·阿德勒和最近由基思·沃斯利开发的几何工具研究了这一点。我在这个领域的工作已经产生了(I)一个被称为高斯运动学公式的几何工具，它统一和简化了许多现有的关于随机场的文献，以及(Ii)在一般情况下近似精度的最强已知结果。我建议使用这些工具来研究由鞍点型近似产生的新的随机场的非高斯模型以及稳定的随机场。我还建议研究这些近似在高维中的行为，以及它们与大型随机矩阵的关系。这些结果将在非高斯脑成像数据的研究以及高维推理中得到应用。解决这个问题的另一种方法是使用经验贝叶斯技术，通常被称为错误发现率(FDR)技术。我在这个领域的工作主要集中在对FDR的渐近控制以及对FDR有用的汇总统计数据：错失率和p值集合的尾部强度。在这个提议中，我建议通过将同时推理问题修改为识别脑成像数据中固有的空间结构的问题来扩展Genovese和Wasserman在随机场FDR方面的工作。为了使解决同时推理问题的统计方法的任何进步对大脑成像社区有用，它们必须集成到研究人员的软件环境中。这份提案中描述的所有统计技术都将整合到NiPy中，这是一个多中心神经成像软件项目，我是该项目的主要开发者之一。