Inference methods in imaging neuroscience

This thesis concerns the statistical characterisation of neuroimaging data; namely the detection of statistically surprising (significant) responses in measured brain activity that is continuous in space and time. It illustrates the application of these precedures developed using functional magnetic resonance time series of blood oxygenation level dependent (BOLD) signals. The spatio-temporal dynamics of BOLD reflects brain metabolism via the neurovascular coupling, and is therefore of interest to neuroscience. This coupling ensures that local use of oxygen relates to local supply, largely via the inflow of blood. As a physical measure of these fluid dynamics, BOLD unfolds in continuous space-time. In practice however, assessing experimental effects on BOLD requires statistical inference, which is not practical for continuous four-dimensional representations. This thesis contributes four ideas for statistical inference on the neuronal causes of BOLD. Each retains some reduced notion of continuity (in either space or time). The first three Chapters consider ‘spatial’ and ‘topological’ inference on atemporal transformations of the original four-dimensional data. Here, we assume measurements have already been collapsed over time at each sampled point of space via inversion of a General Linear Model; the resulting ‘SPM’ estimates the true field of parameters governing experimentally-induced BOLD. Chapters 2-3 concern topological inference on this true underlying field. The aim is to decide on the occurrence of discrete topological features (e.g. the existence of local maxima) using procedures whose error-rate is known/controlled. Chapter 4 aims to infer experimentally induced patterning in the spatial organisation of topological events (clusters or peaks) in an SPM. Chapter 5 then revisits the temporal dynamics between neuronal populations, whose spatial locations have been determined in advance, and attempts to understand their structure. Chapter 6 concludes this thesis. It summarizes the limitations of our proposed methods and explores their future extension and generalisation