Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior

• Published in: NeuroImage (Orlando, Fla.) Vol. 50; no. 1; pp. 150 - 161
• Main Authors: van Gerven, Marcel A.J., Cseke, Botond, de Lange, Floris P., Heskes, Tom
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.03.2010; Elsevier Limited
• Subjects: Algorithms; Bayes Theorem; Bayesian analysis; Bayesian inference; Brain - physiology; Databases as Topic; Expectation propagation; Feasibility Studies; Humans; Logistic Models; Logistic regression; Logistics; Magnetic Resonance Imaging - methods; Medical imaging; Methods; Multivariate Analysis; Multivariate Laplace distribution; Photic Stimulation; Reading; Signal Processing, Computer-Assisted; Sparsity; Time Factors; Time series; Visual Perception - physiology; Expectation propagation; Logistic regression; Multivariate Laplace distribution; Multivariate analysis; Bayesian inference
• ISSN: 1053-8119; 1095-9572; 1095-9572
• DOI: 10.1016/j.neuroimage.2009.11.064

Bayesian logistic regression with a multivariate Laplace prior is introduced as a multivariate approach to the analysis of neuroimaging data. It is shown that, by rewriting the multivariate Laplace distribution as a scale mixture, we can incorporate spatio-temporal constraints which lead to smooth importance maps that facilitate subsequent interpretation. The posterior of interest is computed using an approximate inference method called expectation propagation and becomes feasible due to fast inversion of a sparse precision matrix. We illustrate the performance of the method on an fMRI dataset acquired while subjects were shown handwritten digits. The obtained models perform competitively in terms of predictive performance and give rise to interpretable importance maps. Estimation of the posterior of interest is shown to be feasible even for very large models with thousands of variables.