Information measures on discrete spaces

I will discuss recent work considering the issue of how Fisher Information should be defined on the integers, and on the set $\{0,1,\dots ,n\}$, motivated by the maximum entropy property of the Poisson and binomial distributions. I will show that the resulting information measures have useful properties which parallel those of the Fisher information with respect to a real location parameter, suggesting that they too can form a basis for Information Geometry, suggesting a form for geodesics related to transportation problems.

(This talk is based on joint work with Harremoës, Hillion, Kontoyiannis, Madiman and Yu).