  This is a follow-up of a previous article where we proved local stability
estimates for a potential in a Schr\"odinger equation on an open bounded set in
dimension $n=3$ from the Dirichlet-to-Neumann map with partial data. The region
under control was the penumbra delimited by a source of light outside of the
convex hull of the open set. These local estimates provided stability of
log-log type corresponding to the uniqueness results in Calder\'on's inverse
problem with partial data proved by Kenig, Sj\"ostrand and Uhlmann. In this
article, we prove the corresponding global estimates in all dimensions higher
than three. The estimates are based on the construction of solutions of the
Schr\"odinger equation by complex geometrical optics developed in the
anisotropic setting by Dos Santos Ferreira, Kenig, Salo and Uhlmann to solve
the Calder\'on problem in certain admissible geometries.
