Granger causality for mixed time series generalized linear models: A case study on multimodal brain connectivity

This paper is motivated by neuroscience studies aimed at understanding causal or predictive interactions between nodes in a brain network using multimodal brain activity data. To assess Granger causality, we introduce a flexible framework through a general class of models that accommodate mixed types of data (binary, count, continuous and positive components) formulated in a generalized linear model (GLM) fashion. To conduct statistical inference for causality, we propose a Bayesian mixed time series model that incorporates spike-and-slab priors on selected parameters. This framework enables effective selection of causal ordering and offers robust uncertainty quantification. The proposed methods are then applied to brain activity data, including both spike train and local field potential (LFP) activity, recorded as animals (rats) performed a complex sequence memory task. The proposed methodology provides critical insights into the causal relationship between band-specific spectral power in the LFP and subsequent spiking activity. Specifically, power in the LFP beta band is predictive of spiking activity 300 milliseconds later, providing a novel analytical tool for this area of emerging interest in neuroscience and demonstrating its usefulness and flexibility in the study of causality in general.