A weakly informative prior for Bayesian dynamic model selection with applications in fMRI

TL;DR

This paper introduces a Bayesian dynamic model with a novel weakly informative prior for analyzing fMRI data, effectively capturing brain connectivity with sparsity and robustness.

Contribution

It proposes a new weakly informative prior for state variances in Bayesian dynamic models, tailored for sparse and high-frequency fMRI data analysis.

Findings

Effective in identifying sparse brain connectivity patterns

Produces proper posterior predictive results

Demonstrated through simulations and real fMRI data

Abstract

In recent years, Bayesian statistics methods in neuroscience have been showing important advances. In particular, detection of brain signals for studying the complexity of the brain is an active area of research. Functional magnetic resonance imagining (fMRI) is an important tool to determine which parts of the brain are activated by different types of physical behavior. According to recent results there is evidence that the values of the connectivity brain signal parameters are close to zero and due to the nature of time series fMRI data with high frequency behavior, Bayesian dynamic models for identifying sparsity are indeed far-reaching. We propose a multivariate Bayesian dynamic approach for model selection and shrinkage estimation of the connectivity parameters. We describe the coupling or lead-lag between any pair of regions by using mixture priors for the connectivity parameters and propose a new weakly informative default prior for the state variances. This framework produces one-step-ahead proper posterior predictive results and induces shrinkage and robustness suitable for fMRI data in the presence of sparsity. To explore the performance of the proposed methodology we present simulation studies and an application to functional magnetic resonance imaging data.