Computational Information Geometry Wonderland

In information theory, there exists several notions of information such as Fisher information in Statistics or Shannon information in Coding theory. Those various definitions gained momentum by asking questions like "How hard is it to estimate/discriminate distributions?" (Fisher) or "How hard is it to compress data?" (Shannon). Those "how hard..." questions were answered by proving lower bounds (Cram\'er-Rao for Fisher, and Entropy for Shannon). Similarly, Chernoff information answers the "How hard is it to classify (empirical) data?" by providing a tight lower bound: the (Chernoff) (classification) information.

So the question is which question and which lower bound we can prove to define novel information measures?
Frank.