Statistics and tropicalization of local field Gaussian measures

2019/09/02 by Maazouz, Yassine El, Tran, Ngoc Mai
#12J25 #14T90 #60E05 #62H05 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1909.00559

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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