Fig. 9.

Model performance comparisons through posterior predictive checks and cross validations between conventional univariate GLM (A) and BML (B). The subfigures A and B show the posterior predictive density overlaid with the raw data from the 124 subjects at the 21 ROIs for GLM and BML, respectively: solid black curve is the raw data at the 21 ROIs with linear interpolation while the fat curve in light blue is composed of 500 sub-curves each of which corresponds to one draw from the posterior distribution based on the respective model. The differences between the solid black and light blue curves indicate how well the respective model fits the raw data. BML fitted the data clearly better than GLM at the peak and both tails as well as the skewness because pooling the data from both ends toward the center through shrinkage clearly validates our adoption of BML. To make performance comparisons possible, the conventional univariate GLM was Bayesianized with a noninformative prior (i.e., uniform distribution on (− ∞, + ∞)) for the regions. Reprinted from Chen et al. (2019a).