Fig. 7.

Posterior distributions of the slope effect derived from BML with 124 subjects at 21 regions. The density plot and the associated posterior interval at each region were based on random draws from the same overall high-dimensional posterior distribution that was numerically simulated from the BML model. The vertical blue line indicates zero effect; orange and green tails mark the regions beyond the 90% and 95% uncertainty (compatibility or quantile) intervals, respectively. If results highlighting is desirable, one can claim the regions with strong evidence of slope effect as the blue line being within the color tails, as indicated with orange and green dot-dashed boxes. Compared to the conventional confidence interval that is flat and inconvenient to interpret, the posterior density provides much richer information about each effect such as spread, shape and skewness. Relative to the conventional whole-brain voxel-wise analysis that rendered with only two surviving clusters (Xiao et al., 2019) based on the primary voxel-wise p-value threshold of 0.001, the BML showed a much higher inference efficiency with 8 regions that could be highlighted with strong evidence. To illustrate the conventional dichotomization pitfall through a common practice of thresholding at 0.05, the region of L SFG also elicited some extent of slope effect with a moderate amount of statistical evidence: the probability that its effect is greater than zero is about 0.93 conditional on the data and the BML model. Reprinted from Chen et al. (2019b).