Multilevel linear modelling for FMRI group analysis using Bayesian inference

• Published in: NeuroImage (Orlando, Fla.) Vol. 21; no. 4; pp. 1732 - 1747
• Main Authors: Woolrich, Mark W., Behrens, Timothy E.J., Beckmann, Christian F., Jenkinson, Mark, Smith, Stephen M.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.04.2004; Elsevier Limited
• Subjects: Bayes; Bayes Theorem; Bayesian analysis; Brain - physiology; Computer Simulation - statistics & numerical data; Economic models; Evoked Potentials - physiology; FMRI; GLM; Humans; Hypotheses; Image Interpretation, Computer-Assisted; Linear Models; Magnetic Resonance Imaging; Markov Chains; Mathematical Computing; Medical imaging; Mixed effects; Monte Carlo Method; Motor Activity - physiology; Multivariate Analysis; Noise; Probability; Random effects; Reference priors; Statistics; Mixed effects; Random effects; GLM; Reference priors; FMRI; Bayes
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2003.12.023

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 (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial 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 neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an information-theoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.