  Concepts from information geometry are used to analyse parameter sensitivity
for a nuclear energy density functional, representative of a class of
semi-empirical functionals that start from a microscopically motivated ansatz
for the density dependence of the energy of a system of protons and neutrons.
It is shown that such functionals are sloppy, characterized by an exponential
range of sensitivity to parameter variations. Responsive to only a few stiff
parameter combinations, they exhibit an exponential decrease of sensitivity to
variations of the remaining soft parameters. By interpreting the space of model
predictions as a manifold embedded in the data space, with the parameters of
the functional as coordinates on the manifold, it is also shown that the
exponential distribution of model manifold widths corresponds to the
distribution of parameter sensitivity. Using the Manifold Boundary
Approximation Method, we illustrate how to systematically construct effective
nuclear density functionals of successively lower dimension in parameter space
until sloppiness is eventually eliminated and the resulting functional contains
only stiff combinations of parameters.
