A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes

TL;DR

This paper introduces a Bayesian heteroscedastic GLM for fMRI data that adaptively accounts for motion spikes, improving detection of brain activity by modeling variance changes over time.

Contribution

It develops a Bayesian voxel-wise GLM with autoregressive noise and variable selection, enabling automatic down-weighting of motion spikes and simultaneous inference of lag order.

Findings

GLMH detects more brain activity than homoscedastic models.

Model effectively down-weights motion spikes.

Variance modeling improves fMRI analysis accuracy.

Abstract

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explanatory variables in both the mean and variance (e.g., time trends, activation stimuli, head motion parameters and their temporal derivatives), and to compute the posterior probability of inclusion from the MCMC output. Variable selection is also applied to the lags in the autoregressive noise process, making it possible to infer the lag order from the data simultaneously with all other model parameters. We use both simulated data and real fMRI data from OpenfMRI to illustrate the importance of proper modeling of heteroscedasticity in fMRI data analysis. Our results show that the GLMH tends to detect more brain activity, compared to its homoscedastic counterpart, by allowing the variance to change over time depending on the degree of head motion.