  Gaussian graphical models represent the backbone of the statistical toolbox
for analyzing continuous multivariate systems. However, due to the intrinsic
properties of the multivariate normal distribution, use of this model family
may hide certain forms of context-specific independence that are natural to
consider from an applied perspective. Such independencies have been earlier
introduced to generalize discrete graphical models and Bayesian networks into
more flexible model families. Here we adapt the idea of context-specific
independence to Gaussian graphical models by introducing a stratification of
the Euclidean space such that a conditional independence may hold in certain
segments but be absent elsewhere. It is shown that the stratified models define
a curved exponential family, which retains considerable tractability for
parameter estimation and model selection.
