Robust brain causality network construction based on Bayesian multivariate autoregression Abstract   Background  Cognitive processes involve information integration among multiple encephalic regions, which can be measured by causal networks. However, the estimation of causal networks by means of some traditional methods with the least square will lead to distorted networks because of the unexpected outlier noise and the small number of signal samples in real applications.    New method  In this work, we adopted Bayesian inference to estimate parameters in a multivariate autoregression model (MVAR), to restrain the influence of outliers.    Results  Through the simulation study, we observed that our proposed method can efficiently suppress outlier influence and shows stable performance when sample sizes become small. Application to real motor imagery functional magnetic resonance imaging (fMRI) also revealed that the proposed approach can capture the inherent hemispheric lateralization of motor imagery even with a small number of fMRI samples.    Comparison with existing methods  We compared our proposed Bayesianbased Granger analysis with traditional Granger causality analysis.    Conclusions  The analyses conducted in the current work demonstrate the robustness of Bayesianbased Granger analysis to outlier conditions or physiological signals with small sample sizes.

Bayesian fusion and multimodal DCM for EEG and fMRI Abstract   This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors xe2x80x93 derived from dynamic causal modelling (DCM) of EEG data xe2x80x93 for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters xe2x80x93 as measured by the KullbackLeibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proofofprinciple that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation.