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