Causality in Time Series - ClopiNet

Roebroeck Seth Valdes-Sosaand cortical columns. First, the fusion of multiple imaging modalities, possibly simultaneouslyrecorded, has received a great deal of attention. Particularly, several attemptsto model-driven fusion of simultaneousy recorded fMRI and EEG data, by inverting aseparate observation model for each modality while using the same underlying neuronalmodel, have been reported (Deneux and Faugeras, 2010; Riera et al., 2007; Valdes-Sosaet al., 2009). This approach holds great potential to fruitfully combine the superior spatialresolution of fMRI with the superior temporal resolution of EEG. In (Valdes-Sosaet al., 2009) anatomical connectivity information obtained from diffusion tensor imagingand fiber tractography is also incorporated. Second, advances in MRI technology,particularly increases of main field strength to 7T (and beyond) and advances in parallelimaging (de Zwart et al., 2006; Heidemann et al., 2006; Pruessmann, 2004; Wiesingeret al., 2006), greatly increase the level spatial detail that are accessible with fMRI. Forinstance, fMRI at 7T with sufficient spatial resolution to resolve orientation columns inhuman visual cortex has been reported (Yacoub et al., 2008).The development of state space models for causal analysis of fMRI data has movedfrom discrete to continuous and from deterministic to stochastic models. Continuousmodels with stochastic dynamics have desirable properties, chief among them a robustinference on causal influence interpretable in the WAGS framework, as discussedabove. However, dealing with continuous stochastic models leads to technical issuessuch as the properties and interpretation of Wiener processes and Ito calculus (Friston,2008). A number of inversion or filtering methods for continuous stochastic modelshave been recently proposed, particularly for the goal of causal analysis of brain imagingdata, including the local linearization and innovations approach (Hernandez et al.,1996; Riera et al., 2004), dynamic expectation maximization (Friston et al., 2008) andgeneralized filtering (Friston et al., 2010). The ongoing development of these filteringmethods, their validation and their scalability towards large numbers of state variableswill be a topic of continuing research.AcknowledgmentsThe authors thank Kamil Uludag for comments and discussion.ReferencesOdd O. Aalen. Dynamic modeling and causality. Scandinavian Actuarial journal,pages 177–190, 1987.O.O. Aalen and A. Frigessi. What can statistics contribute to a causal understanding?Board of the Foundation of the Scandinavian journal of Statistics, 34:155–168, 2007.G. K. Aguirre, E. Zarahn, and M. D’Esposito. The variability of human, bold hemodynamicresponses. Neuroimage, 8(4):360–9, 1998.H Akaike. On the use of a linear model for the identification of feedback systems.Annals of the Institute of statistical mathematics, 20(1):425–439, 1968.96