Information geometry aims to apply the techniques of differential geometry to statistics?. Often it is useful to think of a family of probability distributions as a statistical manifold. For example, normal distributions form a 2-dimensional manifold, parameterised by , mean and standard deviation. On such manifolds there are notions of Riemannian metric, connection, curvature, and so on, of statistical relevance.
One of the founders of the subject is Shun-ichi Amari.
Tim Porter: I have looked briefly at the Methods of Info Geom book and it seemed to me to be distantly related to what the eminent statistician David Kendall used to do. He and some coauthors wrote a very nice book called: Shape and Shape Theory (nothing to do with Borsuk’s Shape Theory). The theory may be of relevance as it used differential geometric techniques. (Incidently there are some nice questions concerning the space of configurations of various types that would be a good source for student project work in it.)
My query is whether the link is a strong one between the Amari stuff and those Kendall Shape space calculations. Kendall’s theory and some similar work by Bookstein is widely used in identifcation algorithms using a feature space. In case the link is only faint I will leave it at that for the moment. Any thoughts anyone?
Eric: I wrote some stuff here, which is now relegated to Revision 5. I’ve rewritten most of the material here.