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Invariant geometric structures on statistical models
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SYSNO ASEP 0449264 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Invariant geometric structures on statistical models Author(s) Schwachhöfer, L. (DE)
Ay, N. (DE)
Jost, J. (DE)
Le, Hong-Van (MU-W) RID, SAI, ORCIDSource Title Geometric Science of Information. - Cham : Springer, 2015 / Nielsen F. ; Barbaresco F. - ISBN 978-3-319-25039-7 Pages s. 150-158 Number of pages 9 s. Publication form Online - E Action International Conference on Geometric Science of Information (GSI) 2015 /2./ Event date 28.10.2015-30.10.2015 VEvent location Palaiseau Country FR - France Event type WRD Language eng - English Country CH - Switzerland Keywords geometric structures ; statistical models Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000374288700017 EID SCOPUS 84950311310 DOI 10.1007/978-3-319-25040-3_17 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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