Robust Bayesian general linear models

We describe a Bayesian learning algorithm for Robust General Linear Models (RGLMs). The noise is modeled as a Mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides a robust estimation of regression coefficients. A variational inference framework is used to prevent overfitting and provides a model order selection criterion for noise model order. This allows the RGLM to default to the usual GLM when robustness is not required. The method is compared to other robust regression methods and applied to synthetic data and fMRI.