  Information geometry can be used to understand and optimize Higgs
measurements at the LHC. The Fisher information encodes the maximum sensitivity
of observables to model parameters for a given experiment. Applied to
higher-dimensional operators, it defines the new physics reach of any LHC
signature. We calculate the Fisher information for Higgs production in weak
boson fusion with decays into tau pairs and four leptons, and for Higgs
production in association with a single top quark. In a next step we analyze
how the differential information is distributed over phase space, which defines
optimal event selections. Conversely, we consider the information in the
distribution of a subset of the kinematic variables, showing which production
and decay observables are the most powerful and how much information is lost in
traditional histogram-based analysis methods compared to fully multivariate
ones.
