Abstract: Non-invasive neuroimaging is a powerful tool to study human cognition. For fast and complex cognitive processes, both spatial and temporal resolutions are important. Magnetoencephal​ography (MEG) and electroencephal​ogram (EEG) measure changes in magnetic fields or voltages induced by neural activity, with high temporal resolution. However, because the recordings reflect integrations of neural activities all over the brain, we need to solve a highly underspecified source localization problem, to analyze the spatial properties of neural signals in the brain source space. In this thesis, we aim to improve statistical models for MEG/EEG source space analysis, to achieve better inference to understand the neural basis of complex cognitive processes. Although various models have been proposed for source localization, the theoretical properties of the problem, such as the fundamental limits of spatial resolution, are less studied. We first propose to explore these properties, with both theoretical analysis and systematic empirical simulations, as guidance for practice. For MEG/EEG experiments, source localization is often an intermediate step; researchers are more interested in quantifying the dependence between the source signals and designed covariates, or the connectivity between different brain regions. Naive two-step approaches obtain the source solutions with default methods first, and then run the second-step analysis. However, inappropriate regularization in the first step can lead to inaccurate inference. Here we propose one-step models that jointly solve source localization and the second-step analysis. In our completed work, to quantify the correlation between spatio-temporal source signals and covariates, we developed a one-step regression model within the source localization frame work, where the time-frequency components representing the source time series were regressed against the covariates, subject to structured sparsity-induci​ng penalties. Compared with a naive default two-step method, the model produced more accurate and interpretable results in both simulated and real data. Along this direction, we propose more flexible Bayesian one-step models, where spatio-temporal regularity and prior knowledge can be incorporated, to quantify the dependence between source signals and covariates, and the connectivity between brain regions. We will apply the one-step methods to study visual scene understanding. Previous work suggests that the human visual cortex is hierarchically organized, and different brain areas extract information from low-level edge orientations to high-level semantic features. However, the details of what features are extracted in intermediate areas are unclear. Moreover, scene understanding involves fast processing of rich information, and thus may involve strong top-down feedback along the hierarchy. Yet a detailed examination of the feedback effect remains missing. Here, by analyzing MEG/EEG recordings when human subjects process various visual scenes, we plan to provide a spatio-temporal profile of dependence between the neural signals and modern computer vision features, at low-, mid- and high-levels, to help search for the best candidate model of intermediate processing, and shed light on the the feedback effects. Additionally, we will directly quantify the connectivity at different temporal stages between relevant brain areas as further depiction of the top-down feedback effects. Thesis Committee: Robert Kass (co-chair) Michael Tarr (co-chair) Geoff Gordon, Pulkit Grover, Matti Hamalainen (Harvard)