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A Homotopical Geometry of the Multinomial and Negative-Multinomial Potentials
We study the one-parameter family of Hessian metrics $g_α=αh_++(1-α)h_-$, $α\in[0,1]$, formed by convexly combining the log-partition functions (not the densities) of the multinomial and negative multinomial Fisher information Hessians. Four results are proved in full. (1) $g_α\succ0$ for all $α\in[
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