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- W2967984911 abstract "We provide an alternative differential geometric framework of the manifold $$mathbb M$$ of parametric statistical models. While adopting the Fisher-Rao metric as the Riemannian metric g on $$mathbb M$$ , we treat the original parameterization of the statistical model as affine coordinate chart on the manifold endowed with a flat connection, instead of using a pair of torsion-free affine connections with generally non-vanishing curvature. We then construct its g-conjugate connection which, while necessarily curvature-free, carries torsion in general. So instead of associating a statistical structure to $$mathbb M$$ , we construct a statistical manifold admitting torsion (SMAT). We show that $$mathbb M$$ is dually flat if and only if torsion of the conjugate connection vanishes." @default.
- W2967984911 created "2019-08-22" @default.
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- W2967984911 date "2019-01-01" @default.
- W2967984911 modified "2023-10-16" @default.
- W2967984911 title "New Geometry of Parametric Statistical Models" @default.
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- W2967984911 doi "https://doi.org/10.1007/978-3-030-26980-7_30" @default.
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