Computational Information Geometry Wonderland

The seminal paper of Rao written before he joined Cambridge for his PhD is available online at:

Breakthroughs in Statistics
page 235 is a reprint of:
Rao, Calyampudi (1945). "Information and the accuracy attainable in the estimation of statistical parameters". Bulletin of the Calcutta Mathematical Society 37: 81?89.

There we find three essential results:

• Cramer-Rao bound

• Population space and riemannian geometry using the Fisher information metric as the quadratic differential form.

• Test of significance (and classification)

Information geometry has since then spreaded, with the work of Chentsov on alpha-connections and its investigation by Amari. Historically, the space of distributions, was called the "population space".

The Rao distance for 1D normals is also given.

Frank.