Inference for smooth stochastic processes with applications to neuroimaging

摘要：乔纳森·泰勒提议：0405970本提案的重点是研究光滑向量值随机场的命中概率与独立，同分布的高斯过程作为组件。这些模型可以用来构建各种非高斯实值过程，尽管它们与高斯过程密切相关。过程的平滑性使得许多来自点过程的工具可以用于研究这些命中概率。这些点过程，基于过程的临界点产生一个明确的表示命中概率以及准确的近似，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对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应该对研究其他非高斯模型很有用。这个建议的实际动机是在其应用程序中估计的家庭明智的错误率（FWER）在神经成像激活研究。这个FWER在确定神经影像学研究中哪些区域与给定的实验任务相关方面很重要。在这些研究中，心理学家能够收集人类大脑中激活的时空记录（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，这些任务可能是视觉任务，听觉任务等。在收集了数据之后，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。这个建议的结果帮助心理学家做出这个决定，允许心理学家只接受预先指定的FWER结果。该建议建立在文献中的早期结果，并将其扩展到更复杂的激活模型。

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.