Statistics and tropicalization of local field Gaussian measures

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.

15 pages, 4 figures

References in corpus (1)

• Tropical Principal Component Analysis and its Application to Phylogenetics

Cited by in corpus (1)

• The Gaussian entropy map in valued fields