Goodness-of-fit testing and independent component analysis with applications to cognitive neuroscience

统计学是一门从数据中获取信息的强大学科，它已被应用于许多其他科学领域。从这个角度来看，神经科学是一个新的、迷人的研究领域，它专注于研究动物或人类的大脑行为。很自然，统计学家已经开始向该领域的研究人员提供他们的技能。本提案旨在为这一努力作出我的贡献。本建议包括两部分。第一个是致力于开发新的拟合优度程序，使用基于经验特征函数的过程或在多变量时间序列模型的背景下开发。另一个方面是新的创新独立成分分析（ICA）方法的发展。本部分构建的工具将用于通过功能磁共振成像（fMRI）数据的模型构建来帮助理解我们的大脑行为。例如，ICA是利用许多随机变量之间的依赖关系的最新且强大的探索技术。它们可以用来探索在功能磁共振成像实验中收集的大量数据集，它们可以被视为对其他更具验证性的技术的良好补充。在最后一个项目中开发的所有方法都将在AnalyzeFMRI R包中实现。

Statistics is a powerful discipline that deals with gaining information from data and it has been applied to many other fields of science. In that perspective, neuroscience is a new and fascinating field of research that focuses on the study of the animal or human brain behaviour. And it is very naturally that statisticians have begun to offer their skills to researchers of the field. This proposition is devoted to add my contribution to this effort. The present proposal contains two parts. The first one is dedicated to the development of new goodness-of-fit procedures, using empirical characteristic function based processes or developed in the context of multivariate time series models. Another aspect is the development of new innovative Independent Component Analysis (ICA) Methods. The tools built in this part will be used to help understanding our brain's behaviour through model building of functional Magnetic Resonance Imaging (fMRI) data. For example, ICA are recent and powerful exploratory techniques exploiting the dependencies between many random variables. They can be used to explore the huge data sets collected during fMRI experiments and they can be seen as a good complement to other more confirmatory techniques. All the methods developed in this last project will be implemented into the AnalyzeFMRI R package.