Titlebook: Geometric Structures of Information; Frank Nielsen Book 2019 Springer Nature Switzerland AG 2019 Hessian Information Geometry.Shape Space.

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Statistical Manifolds Admitting Torsion and Partially Flat Spaces,e-contrast function. The aim of this paper is to summarize such previous results. In particular, we focus on a partially flat space, which is a statistical manifold admitting torsion where one of its dual connections is flat. In this space, it is possible to discuss some properties similar to those

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Frank NielsenFeatures new and fruitful interactions between several branches of science: information science, mathematics and physics.Addresses interrelations between different mathematical domains like shape spac

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Springer Nature Switzerland AG 2019

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Geometric Structures of Information978-3-030-02520-5Series ISSN 1860-4862 Series E-ISSN 1860-4870

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A Class of Non-parametric Deformed Exponential Statistical Models,t zero. This class generalizes the class introduced by N.J. Newton. We discuss the convexity and regularity of the normalization operator, the form of the deformed statistical divergences and their convex duality, the properties of the escort densities, and the affine manifold structure of the statistical bundle