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external supervisor

Dr. Habib Ganjgahi, Department of Statistics, University of Oxford


Functional Magnetic Resonance Imaging (fMRI) has brought immense insight into our understating of human brain function in health and disease. In an fMRI study, time series of brain activity are measured at each point in the brain, and, after several preprocessing steps, a group of subjects can be analysed together.  In a group analysis standard practice is a meta-analytic approach:  Instead of modelling all subjects’ time series jointly, each subject is analysed in isolation in a “1st level” model, and point estimates and standard errors from each subject are analysed in a “2nd level” model.  However, this approach is not optimal – e.g., 1st  level estimates can never be updated – and standard errors can be inflated.

The linear mixed effect model (LMM) is a widely used and flexible statistical tool that accommodates data from longitudinal & repeated measures designs as well as data fMRI data. A mainstay in biostatistics, LMMs have generally not been applied to large-scale data like fMRI.  fMRI and other imaging data are intrinsically high-dimensional, and can be a challenge even when n’s are modest. Application of the LMM to fMRI, for example, has been hampered by likelihood optimization via numerical methods that are prone to convergence failure. In addition, random and fixed effects inferences depend on asymptotic distributions that can be perform poorly even for moderate n. Although many analytical techniques have been developed to accelerate the likelihood optimization time, these advances do not eliminate problems with finite-sample inference inaccuracies, multiple testing problem nor convergence failure.

The purpose of this project is to build a computationally efficient model for group fMRI analysis using summary statistic approach and non-iterative random effect estimator for LMM and extent the model for group fMRI analysis with complex designs i.e longitudinal and repeated measures that scales to large studies like the UK Biobank. 


The successful completion of the project will likely produce at least one publication and conference presentations.  At least an undergraduate degree in mathematics, statistics or similar technical subject and good writing skills are required, and will be supplemented by participation in the Academic for PhD Training in Statistics (APTS, candidate requires to participate in APTS and modules related to the project. 


Students with training background in mathematics or statistics; experience with programming. 


  • Thomas Nichols
    Thomas Nichols

    Professor of Neuroimaging Statistics, Nuffield Department of Population Health