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Information geometry began as an investigation of the natural differential geometric structure possessed by families of probability distributions which constitute a statistical model. Essentially the probability distribution is viewed as a manifold. Geometric properties such as a Riemann metric and affine connections are introduced. Interestingly, the ideas of duality (relating different connections) are also incorporated. In addition the notion of Fisher information (generalized as the Fisher information matrix) is employed which defines a metric on the statistical manifold; recall note [#!apdsp5!#] and the beginning of the last section of appendix A.7. Two references are: [#!AN00!#] and [#!MR93!#]. Also [#!Hu98!#] contains a chapter on information geometry within the context of quantum statistics.

jbg
2002-05-26