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arXiv · 2208.06539

Natural differentiable structures on statistical models and the Fisher metric

Hông Vân Lê
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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, $k$-integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.

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Hông Vân Lê. 2022-08-13. Natural differentiable structures on statistical models and the Fisher metric. https://doi.org/10.1007/s41884-022-00090-w

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