Information geometry of Bayes computations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910813783064576 |
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| author | Pistone, Giovanni |
| author_facet | Pistone, Giovanni |
| contents | Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a one-parameter statistical model equals the classical Fisher's score. In the present note, we first offer a concise review of the notion of a statistical bundle as a set of couples of probability densities and Fisher's scores. Then, we show how the nonparametric dually affine setup deals with the basic Bayes and Kullback-Leibler divergence computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information geometry of Bayes computations Pistone, Giovanni Statistics Theory Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a one-parameter statistical model equals the classical Fisher's score. In the present note, we first offer a concise review of the notion of a statistical bundle as a set of couples of probability densities and Fisher's scores. Then, we show how the nonparametric dually affine setup deals with the basic Bayes and Kullback-Leibler divergence computations. |
| title | Information geometry of Bayes computations |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2502.02160 |