Natural differentiable structures on statistical models and the Fisher metric
arXiv:2208.06539 · doi:10.1007/s41884-022-00090-w
Abstract
In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of measures, -integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.
22p. submitted version to Information Geometry