In this article, we focused on developing the conditionally Gaussian hierarchical Bayesian model (CG-HBM), which forms a superclass of several inversion methods for source localization of brain activity using somatosensory evoked potential (SEP) and field (SEF) measurements. The goal of this proof-of-concept study was to improve the applicability of the CG-HBM as a superclass by proposing a robust approach for the parametrization of focal source scenarios. We aimed at a parametrization that is invariant with respect to altering the noise level and the source space size. The posterior difference between the gamma and inverse gamma hyperprior was minimized by optimizing the shape parameter, while a suitable range for the scale parameter can be obtained via the prior-over-measurement signal-to-noise ratio, which we introduce as a new concept in this study. In the source localization experiments, the primary generator of the P20/N20 component was detected in the Brodmann area 3b using the CG-HBM approach and a parameter range derived from the existing knowledge of the Tikhonov-regularized minimum norm estimate, i.e., the classical Gaussian prior model. Moreover, it seems that the detection of deep thalamic activity simultaneously with the P20/N20 component with the gamma hyperprior can be enhanced while using a close-to-optimal shape parameter value.
Bayesian Spatial Inversion and Conjugate Selection Gaussian Prior Models
