Fig. 4.

Gaussian process generative model of local gray matter volume using 1238 healthy adult subjects with ages 18–94 years. (A) The estimated local noise term $\mathit{log}\left(\widehat{\mathit{\sigma }}\right)$ of the GP model for data after smoothing with 8 mm Gaussian kernel is shown. The noise term captures unexplained variability of gray matter volume observations. Red and blue indicate larger vs. smaller local noise variance, respectively. (B) Shown is the relationship of local model evidence and the noise term $\mathit{log}\left(\widehat{\mathit{\sigma }}\right)$ (log log plot) across all voxels for different degrees of smoothing (left). In particular, by applying Gaussian kernels of 4 (red), 8 (blue), and 12 (green) mm FWHM. Additionally histograms of the corresponding indices are shown. The relationship of local model evidence and the standard deviation of gray matter volume observations (log log plot) across all voxels is shown for different degrees of smoothing (right). (C) Histogram of voxelwise length scale parameters l₁^(j) of the input variables obtained from model optimization. (D) 100 random voxel lifespan gray matter volume trajectories of the estimated generative model. Shown is g(x, θ_j) as a function of subject's age.