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Invariant geometric structures on statistical models
Publikationstyp
Conference Paper
Date Issued
2015-10
Sprache
English
First published in
Number in series
9389 LNIP
Start Page
150
End Page
158
Citation
Lecture Notes in Computer Science 9389 LNIP: 150-158 (2015)
Contribution to Conference
Publisher DOI
Scopus ID
Publisher
Springer
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.
DDC Class
004: Informatik
510: Mathematik