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

统计学是一门处理从数据中获取信息的强大学科，它已经被应用到许多其他科学领域。从这个角度来看，神经科学是一个新的、令人着迷的研究领域，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。这一命题致力于为这一努力增添我的贡献。目前的建议包括两个部分。第一个是致力于开发新的拟合度程序，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。另一个方面是创新的独立成分分析(ICA)方法的发展。在这一部分中构建的工具将通过建立功能磁共振成像(FMRI)数据的模型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相关性的最新和强大的探索性技术。它们可以用来探索在功能磁共振实验中收集的巨大数据集，它们可以被视为对其他更具验证性的技术的很好补充。最后一个项目中开发的所有方法都将被实施到AnalyzeFMRI R包中。

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.