Functional brain imaging technologies produce high dimensional data with structured dependency spanning along multiple dimensions. This dissertation focuses on the specific case of Electroencephalography (EEG), even though most methodological developments are applicable to other imaging modalities. The overarching goal is to provide methodological foundations to inferential problems involving population inference in the setting of cognitive experiments. Specifically, I address important challenges associated with the highly heterogenous nature of brain imaging measurements, by reframing complex inferential questions in the context of familiar analytical techniques involving regression, clustering, functional and longitudinal data analysis. These contributions focus on spatio-temporal modeling of EEG measurements, which characterize both intra- and inter-subjects variation within the contexts of neuronal synchronicity and differential band power dynamics. The methodological developments are used to provide analytical insight in several neuro-cognitive studies based on EEG data.