All of the details in the text which were referenced as Supplementary Material are provided in this file. This includes details of: (a) computation of the Karcher mean, (b) full posterior distribution, (c) calibration of pathway scores, (d) utility of densities as predictors, (e) inference on group-level indicator; and results of the analysis to assess sensitivity in (f) the parameter estimates based on the choice of hyperparameters, (g) the estimated principal component bases based on the sample composition, and (h) the density estimates based on the choice of bandwidth.