FMRIB Technical Report TR03MW1

(A related paper has been accepted for publication in Neuroimage)

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),

Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,

Headley Way, Headington, Oxford, UK

* First two authors contributed equally to this work

Corresponding author is Mark Woolrich: woolrich@fmrib.ox.ac.uk

Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a General Linear Model at each level of the hierarchy introducing different random effects variance components. Inferring on these models is non-trivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and top-level regression parameters. Due to the typically small numbers of sessions or subjects in neuro-imaging the choice of prior is critical. To alleviate this problem we introduce to neuro-image modelling the approach of reference priors, which drives the choice of prior such that it is non-informative in an information-theoretic sense. We propose two inference techniques at the top-level for multi-level hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top-level of multi-level hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a non-central multivariate t-distribution between them.

- Introduction

- Model

- Inference
- Bayesian Inference
- Priors and Reference Analysis
- First-level
- Two-level
- Fast Posterior Approximation
- MCMC
- BIDET
- Contrasts

- Higher-level Models
- Multiple group variances
- Artificial Data

- FMRI data

- Conclusions
- Discussion

- Appendix
- Gamma Distribution
- Multivariate Normal distribution
- Multivariate Non-Central t distribution
- Multivariate Non-central t-distribution fit
- Determining Reference Priors
- Marginalising over in the two-level model
- Fast Approximation Point Estimates

- Bibliography
- About this document ...