Inference for smooth stochastic processes with applications to neuroimaging

平滑随机过程的推理及其在神经影像学中的应用

• 批准号: 0405970
• 负责人: Jonathan Taylor
• 金额: --
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405970&HistoricalAwards=false
• 关键词: Inference; smooth; stochastic; processes; applications

ABSTRACTPI: Jonathan Taylorproposal: 0405970The focus of this proposal is the study hitting probabilities for smooth vector-valued random fields with independent, identically distributed Gaussian processes as components. These models can be used to build a variety of non-Gaussian real-valued processes, though they are closely related to Gaussian processes. The smoothness of the processes allows many tools from point processes to be used in studying these hitting probabilities. These point processes, based on critical points of the process yield an explicit representation for the hitting probability as well as an accurate approximation, the so-called expected Euler characteristic approximation. The proposal seeks to extend recent work of the investigator and collaborators on real-valued Gaussian processes to these non-Gaussian models. Insight gained from these models should prove useful in studying other non-Gaussian models. The practical motivation for this proposal is in its application to estimating the Family Wise Error Rate (FWER) in neuroimaging activation studies. This FWER is important in determining which areas in a neuroimaging study are associated with a given experimental task. In these studies, psychologists are able to collect space-time recordings of activation in the human brain (more precisely, they can record something associated with activation known as the BOLD signal). They are then able to study which areas are activated by their task, which might be a visual task, an auditory task, etc. Having collected the data, the psychologists are faced with the task of determining which perceived activations are true activations. The results of this proposal help psychologists in this decision, by allowing the psychologists to only accept results with a prespecified FWER. The proposal builds on earlier results in the literature, and extends them to more complicated models of activation.

摘要：Jonathan Taylor 提案：0405970 该提案的重点是研究以独立、同分布的高斯过程为组成部分的平滑向量值随机场的命中概率。这些模型可用于构建各种非高斯实值过程，尽管它们与高斯过程密切相关。过程的平滑性允许使用来自点过程的许多工具来研究这些命中概率。这些点过程基于过程的关键点，产生命中概率的明确表示以及精确的近似，即所谓的预期欧拉特征近似。该提案旨在将研究者和合作者最近关于实值高斯过程的工作扩展到这些非高斯模型。从这些模型中获得的见解对于研究其他非高斯模型应该是有用的。该提案的实际动机在于其应用于估计神经影像激活研究中的家庭明智错误率（FWER）。 FWER 对于确定神经影像学研究中的哪些区域与给定的实验任务相关非常重要。在这些研究中，心理学家能够收集人脑激活的时空记录（更准确地说，他们可以记录与激活相关的东西，称为 BOLD 信号）。然后，他们能够研究哪些区域被他们的任务激活，这可能是视觉任务、听觉任务等。收集数据后，心理学家面临的任务是确定哪些感知的激活是真正的激活。该提案的结果允许心理学家仅接受具有预先指定的 FWER 的结果，从而帮助心理学家做出这一决定。该提案建立在文献中的早期结果的基础上，并将其扩展到更复杂的激活模型。