Fig. 6.

Gaussian process models of local and global gray matter volume in the 1238 healthy subject sample. (A) Illustrates the GP based generative model of local GMV in a single voxel in hippocampus (24, − 12, − 18) mm MNI. Columns indicate the dependency on age and total gray matter volume (tgmv, left) total white matter volume (twmv, middle) and total cerebrospinal fluid volume (tcsf, right) respectively. Depicted are 3D surface plots of model components, continuously shown over test locations in input dimensions. Posterior distribution of latent variables $\mathit{g}\left(\mathbf{x},\widehat{\mathit{\theta }}\right)$ with expectation $\overline{\mathit{g}}$ (red) and standard deviation $\overline{\mathit{g}}\pm 1.96\mathit{std}\left(\mathit{g}\right)$ (green) is shown. The likelihood model standard deviations σ = std(ϵ) is shown at $\overline{\mathit{g}}\pm 1.96\mathit{\sigma }$ (gray). (B) Illustrates the GP based generative model of tgmv (left), twmv (middle) and tcsf (right). Columns indicate total intracranial volume (ticv) and age respectively.