  We describe a method, that we call data projection onto parameter space
(DPPS), to optimize an energy functional of the electron density, so that it
reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes
theorem, constrains the optimized functional not to depart unphysically from
existing ab initio functionals. The resulting functional maximizes the
probability of being the \correct" parametrization of a given functional form,
in the sense of Bayes theory. The application of DPPS to water sheds new light
on why density functional theory has performed rather poorly for liquid water,
on what improvements are needed, and on the intrinsic limitations of the
generalized gradient approximation to electron exchange and correlation.
Finally, we present tests of our water-optimized functional, that we call
vdW-DF-w, showing that it performs very well for a variety of condensed water
systems.
