Invariant geometric structures on statistical models

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00449264" target="_blank" >RIV/67985840:_____/15:00449264 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-25040-3_17" target="_blank" >http://dx.doi.org/10.1007/978-3-319-25040-3_17</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-25040-3_17" target="_blank" >10.1007/978-3-319-25040-3_17</a>

Result language
angličtina
Original language name
Invariant geometric structures on statistical models
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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