Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal

摘要

This article concerns the modelling of time-varying and frequency-specificrelationships between two signals, with a focus on intracerebral signalsmeasuring neural activities. Many researchers in neuroscience would like toassess what is called a frequency Granger causality that may vary in time toevalute the functionnal connections between two brain regions during a task. Wepropose the use of an adaptive Kalman filter type of estimator of a linearGaussian vector autoregressive model with coefficients evolving over time. Theestimation procedure is achieved through variational Bayesian approximation andcan be extended for multiple trials. This Bayesian State Space (BSS) modelprovides a dynamical Granger-causality statistic that is quite natural. TheBayesian nature of the model provides a criterion for model order selection andallows us to include prior knowledge in the model. We propose to extend the BSSmodel to include the \`{a} trous Haar decomposition. This wavelet-basedforecasting method, based on a multiple resolution decomposition of the signalusing the redundant \`{a} trous wavelet transform, captures short- andlong-range dependencies between signals and is further used to derive thedesired dynamical and frequency-specific Granger-causality statistic. Theapplication of these models to local field potential data recorded during apsychological experimental task shows the complex frequency based cross-talkbetween amygdala and medial orbito-frontal cortex.