Over local fields, the maximum likelihood Gaussian is the span of the data, conditional independence is an F_q-realizable matroid, and in dimension 2 the tropicalized Gaussian is exactly a supermodular tropical polynomial.
Tropical polyhedra are equivalent to mean payoff games
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Statistics and tropicalization of local field Gaussian measures
Over local fields, the maximum likelihood Gaussian is the span of the data, conditional independence is an F_q-realizable matroid, and in dimension 2 the tropicalized Gaussian is exactly a supermodular tropical polynomial.