  The Fisher Information matrix is a widely used measure for applications
ranging from statistical inference, information geometry, experiment design, to
the study of criticality in biological systems. Yet there is no commonly
accepted non-parametric algorithm to estimate it from real data. In this rapid
communication we show how to accurately estimate the Fisher information in a
nonparametric way. We also develop a numerical procedure to minimize the errors
by choosing the interval of the finite difference scheme necessary to compute
the derivatives in the definition of the Fisher information. Our method uses
the recently published "Density Estimation using Field Theory" algorithm to
compute the probability density functions for continuous densities. We use the
Fisher information of the normal distribution to validate our method and as an
example we compute the temperature component of the Fisher Information Matrix
in the two dimensional Ising model and show that it obeys the expected relation
to the heat capacity and therefore peaks at the phase transition at the correct
critical temperature.

Computation;Computational Physics