Identification of directed influence: Granger causality, kullback-leibler divergence, and complexity

Abstract

Detecting and characterizing causal interdependencies and couplings between different activated brain areas from functional neuroimage time series measurements of their activity constitutes a significant step toward understanding the process of brain functions. In this letter, we make the simple point that all current statistics used to make inferences about directed influences in functional neuroimage time series are variants of the same underlying quantity. This includes directed transfer entropy, transinformation, Kullback-Leibler formulations, conditionalmutual information, and Granger causality. Crucially, in the case of autoregressive modeling, the underlying quantity is the likelihood..