Supervisor: Dr Eftychia Solea
Project description:
Advancements in neuroimaging have made multivariate functional data, represented as vector of random functions, common in medical research. For instance, functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) capture brain activity over time for each region of the brain in every subject within the sample. A problem of significant interest is investigating the interdependencies among the different random functions; analysing the relations among fMRI brain signals is essential for understanding the pathophysiology of neurological diseases.
Despite recent advancements on graphical models for multivariate functional data, most existing statistical studies in this field assume that each observation in the sample is drawn from the same distribution. However, in many applications, it is common to encounter heterogeneous data, that do not form an i.i.d. sample from a single population. For instance, neuroscience studies involve brain activity in a sample of subjects with various subtypes of a neurological diseases. Heterogeneous data also arise when the network structure may depend on a covariate or time. This highlights the need for more rigorous statistical methods that can effectively model data heterogeneity, which has been neglected by current approaches and could provide new insights into our understanding of the network structure. Therefore, the main goal of this project is to develop new statistical methodology and theory for estimating graphical models for heterogeneous multivariate functional data. Specifically, the aims of this project are: (1) joint estimation of nonparametric functional graphical models, (2) functional directed acyclic graphical modelling for heterogeneous functional data, and (3) covariate-adjusted functional graphical modelling to accommodate covariate information. The work will study asymptotic properties of these new estimators in high-dimensions. Open-source software algorithms will be developed and validated using both simulation studies and real fMRI and EEG data. These applications are expected to advance neuroscience by enabling more accurate identification of diverse patient groups across various neurological diseases. This, in turn, will assist clinical researchers in identifying brain disease subtypes and optimising treatment selection
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