Bayesian estimation of directed functional coupling from brain recordings.

Area of Science:

• Time series analysis
• Neuroscience
• Causal inference

Background:

• Assessing causal influences among time series is crucial in many scientific fields, especially neuroscience for understanding brain region interactions.
• Current methods often rely on parametric Granger causality based on linear autoregressive modeling.

Purpose of the Study:

• To propose a novel Bayesian method for linear model identification, termed Gaussian Mixture prior for Expectation Propagation (GMEP).
• To apply GMEP as a linear regression technique within parametric Granger causal inference.
• To leverage structured priors for improved causal inference.

Main Methods:

• GMEP utilizes a Gaussian scale mixture distribution for group sparsity priors, allowing flexible coefficient grouping.
• Approximate posterior inference is performed using Expectation Propagation for coefficients and hyperparameters.
• The method is evaluated on simulated data and empirical fMRI data.

Main Results:

• GMEP demonstrated improved model identification and causal inference when incorporating prior knowledge on sparsity structure.
• Comparisons with standard linear regression methods in simulations showed GMEP's effectiveness.
• Analysis on fMRI data confirmed the benefits of integrating sparsity structure information.

Conclusions:

• GMEP offers a robust Bayesian approach for Granger causal inference, particularly when prior structural information is available.
• The method enhances the accuracy of causal inference in time series, with significant implications for neuroscience.
• Integrating structured priors in Bayesian linear modeling improves the reliability of causal discovery.