Congruent families and invariant tensors

2017/05/31 by Schwachhöfer, Lorenz, Ay, Nihat, Jost, Jürgen +1
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1705.11014

Abstract

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only 2-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant 3-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree n, showing that any family of n-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper.

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