I was recently exposed to the topic of Information Geometry by a friend of mine, and was looking for a good book to begin self-studying this topic. Any suggestions?

Also, what subject matter would one need to have a handle on to begin self-studying this? I have an undergraduate-level background in real analysis, some basic point-set topology, as well as algebra up to the level of Galois Theory.

  • $\begingroup$ It seems books on information geometry are written for an audience already familiar with statistics. The book by Amari and Nagaoka mentioned in the Wikipedia article has an introduction to the required differential geometry, but doesn't do that for statistics. So you'll probably want to have some background in statistics. I'm far from the best person to ask about statistics, but the book by Bickel and Doksum claims to be a suitable introduction for someone at your level of mathematical preparation. You may need to supplement their appendix on basic probability theory with other reading. $\endgroup$ – David Jan 3 '16 at 20:07
  • $\begingroup$ @David: I suggest converting your comment into an answer. $\endgroup$ – J W Feb 19 '16 at 18:20

The most famous book on the subject is probably:

Amari, 2007, Methods of Information Geometry

But there are few other ones that look quite nice:

Amari, 2016, Information Geometry and Its Applications

Murray & Rice, 1993, Differential Geometry and Statistics

Ay et al, 2017, Information Geometry

The last one mentioned is quite new.

This question has been asked quite a few times in different ways on the SE network. Let me link to a few here:

For the background/prerequisites, I would say they are:

  1. Differential geometry: manifold theory (differential forms, connections, etc) and Riemannian geometry (metric and curvature tensors, geodesics, etc)

  2. Probability and statistics: probability distributions, statistical estimation, basic measure theory, and information theory

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