Multivariate statistical analysis of functional neuroimaging data

This dissertation is intended to provide a comprehensive theoretical review and some new developments in the multivariate statistical analysis of functional neuroimaging data. As a stereotypical example of functional imaging techniques, we consider intrinsic optical imaging of the central visual system of mammals, where the spatial pattern of the cortical reflectance is imaged in response to various visual stimulations. We appeal to a general analysis strategy called “pseudo-univariate reduction”, with which the multivariate data distribution is marginalized to a univariate distribution through projection onto some vector. For each choice of projection vector, the resulting one-dimensional distribution can be characterized by some statistic, such as the mean, variance, etc. For a given statistic, one can attempt to optimize its value as a function of the projection vector, and compute an unique set of projection vectors whose univariate distributions have “best” statistical characteristics. We give three particular examples of such a procedure, namely, principal component analysis, canonical variate analysis, and generalized indicator function analysis. First two methods are considered standard in multivariate statistics, and they have been successfully applied to the analysis of functional imaging data. The third method is our original contribution, which we present in the framework of the classical theory of multivariate analysis. We discuss some theoretical and practical advantages of our new method over the existing ones, and demonstrate its efficacy in the analysis of actual functional imaging data of mammalian primary visual cortex.