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Bayesian models for functional magnetic resonance imaging data analysis

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Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This article provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatiotemporal models for fMRI data that detect task‐related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as electroencephalography/magnetoencephalography (EEG/MEG) and diffusion tensor imaging (DTI) data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics. WIREs Comput Stat 2015, 7:21–41. doi: 10.1002/wics.1339 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
Typical fMRI experiment: 3D maps are acquired over time while the subject lies in the scanner, producing time series of fMRI BOLD responses measured at each brain voxel. Selected 2D arrays, corresponding to axial slices across the third dimension, are shown.
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Example of diffusion tensor imaging (DTI) data.
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Effective connectivity. Maximum a posteriori estimates of parameters measuring effective connectivity in an fMRI study on attention to motion (Stephan et al.).
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Functional connectivity. (a) Matrix of posterior estimates of inter‐regional correlations (Bowman et al.); (b) Posterior clustering map of spatially remote voxels (Zhang et al.).
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(a) An Example of PPMs generated with the software SPM8 (http://www.fil.ion.ucl.ac.uk/spm). (b) Design matrix. (c) Overlay of χ2 statistic values showing regions where activity is different between active and rest conditions.
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Typical modeling of the BOLD signal at a given voxel, for both block and event‐related designs. The BOLD signal is modeled as the convolution of the experimental stimulus and the HRF.
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Outline of the Bayesian methods for fMRI data reviewed in this article. Methods are divided according to the objective of the analysis.
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