Invariant geometric structures on statistical models - Hong Van Le, Jürgen Jost, Lorenz Schwachhöfer, Nihat Ay
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last edited by Geo-Sci-InfoAuthor(s): Hong Van Le, Jürgen Jost, Lorenz Schwachhöfer, Nihat Ay
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_17
Video: http://www.youtube.com/watch?v=_1dAY41Z-EM
Slides: Schwachhofer, Invariant geometric structure statistical.pdf
Presentation: https://www.see.asso.fr/node/14331
Creative Commons Attribution-ShareAlike 4.0 InternationalAbstract:
We review the notion of parametrized measure models and tensor fields on them, which encompasses all statistical models considered by Chentsov [6], Amari [3] and Pistone-Sempi [10]. We give a complete description of n-tensor fields that are invariant under sufficient statistics. In the cases n = 2 and n = 3, the only such tensors are the Fisher metric and the Amari-Chentsov tensor. While this has been shown by Chentsov [7] and Campbell [5] in the case of finite measure spaces, our approach allows to generalize these results to the cases of infinite sample spaces and arbitrary n. Furthermore, we give a generalisation of the monotonicity theorem and discuss its consequences.
