A Bayesian heteroscedastic GLM with application to fMRI data with motion spikes

Area of Science:

• Neuroimaging
• Statistical modeling
• Computational neuroscience

Background:

• Functional magnetic resonance imaging (fMRI) data analysis often employs the general linear model (GLM).
• Standard GLM assumes homoscedasticity (constant noise variance), which is frequently violated in fMRI due to factors like head motion.
• Inaccurate noise modeling can lead to reduced sensitivity and biased results in fMRI studies.

Purpose of the Study:

• To propose a novel voxel-wise general linear model with autoregressive and heteroscedastic noise innovations (GLMH) for fMRI data analysis.
• To develop an efficient Bayesian approach, including Markov Chain Monte Carlo (MCMC) methods, for parameter estimation and variable selection.
• To enable data-driven modeling of both the mean and variance components, incorporating various explanatory variables and inferring noise characteristics.

Main Methods:

• A Bayesian voxel-wise general linear model with autoregressive and heteroscedastic noise (GLMH) was developed.
• An efficient Markov Chain Monte Carlo (MCMC) algorithm was implemented for parameter estimation and Bayesian variable selection.
• The model allows for simultaneous selection of regressors for the mean and variance, and inference of autoregressive noise lags.

Main Results:

• The proposed GLMH model effectively down-weights time points affected by motion spikes in a data-driven manner.
• Bayesian variable selection facilitated the inclusion of diverse predictors in both mean and variance models.
• Simulations and real fMRI data analysis demonstrated that GLMH detects more brain activity than homoscedastic models by accounting for temporal variance changes.

Conclusions:

• The GLMH provides a robust framework for fMRI analysis, particularly when dealing with motion artifacts and non-constant noise variance.
• Accounting for heteroscedasticity in fMRI data analysis enhances the detection of neural activity.
• The developed Bayesian MCMC algorithm offers an efficient tool for complex fMRI data modeling and inference.