Granger Causality for Mixed Time Series Generalized Linear Models: A Case Study on Multimodal Brain Connectivity

TL;DR

This paper introduces a Bayesian framework for assessing Granger causality in mixed-type time series data, exemplified by neuroscience data, enabling flexible causal inference across diverse data modalities.

Contribution

It develops a novel Bayesian mixed time series model with spike and slab priors for causality inference in generalized linear models with mixed data types.

Findings

LFP beta power predicts rat spiking activity 300 ms later.

The methodology provides new insights into neural causal relationships.

Demonstrates flexibility in analyzing multimodal brain data.

Abstract

This paper is motivated by studies in neuroscience experiments to understand interactions between nodes in a brain network using different types of data modalities that capture different distinct facets of brain activity. To assess Granger-causality, we introduce a flexible framework through a general class of models that accommodates mixed types of data (binary, count, continuous, and positive components) formulated in a generalized linear model (GLM) fashion. Statistical inference for causality is performed based on both frequentist and Bayesian approaches, with a focus on the latter. Here, we develop a procedure for conducting inference through the proposed Bayesian mixed time series model. By introducing spike and slab priors for some parameters in the model, our inferential approach guides causality order selection and provides proper uncertainty quantification. The proposed methods are then utilized to study the rat spike train and local field potentials (LFP) data recorded during the olfaction working memory task. The proposed methodology provides critical insights into the causal relationship between the rat spiking activity and LFP spectral power. 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.