The nonparametric Fisher geometry and the chi-square process density prior

Understand

It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions.

• Following recent work, we consider the nonparametric generalization of the Fisher geometry.
• The resulting nonparametric Fisher geometry is shown to be equivalent to a familiar, albeit infinite-dimensional, geometric object---the sphere.
• By shifting focus away from density functions and toward \emph{square-root} density functions, one may calculate theoretical quantities of interest with ease.