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arXiv · 1909.00559

Statistics and tropicalization of local field Gaussian measures

Yassine El Maazouz·Ngoc Mai Tran
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Abstract

This paper aims to lay the foundations for statistics over local fields, such as the field of $p$-adic numbers. Over such fields, we give characterizations for maximum likelihood estimation and conditional independence for multivariate Gaussian distributions. We also give a bijection between the tropicalization of such Gaussian measures in dimension 2 and supermodular functions on the 2-dimensional discrete cube. Finally, we introduce the Bruhat-Tits building as a parameter space for Gaussian distributions and discuss their connections to conditional independence statements as an open problem.

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Yassine El Maazouz, Ngoc Mai Tran. 2019-09-02. Statistics and tropicalization of local field Gaussian measures. https://arxiv.org/abs/1909.00559

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