Gaussian Markov Random fields and totally positive matrices

Baz, Juan ; Alonso, Pedro ; Peña, Juan Manuel (Universidad de Zaragoza) ; Pérez-Fernández, Raúl

Resumen: The present paper focuses on the study of the conditions under which the covariance matrix of a multivariate Gaussian distribution is totally positive, paying particular attention to multivariate Gaussian distributions that are Gaussian Markov Random Fields. More specifically, it is proven that, if the graph over which the Gaussian Markov Random Field is defined consists of path graphs and the covariances between adjacent variables on the graph are non-negative, then there always exists a reordering of the variables that renders the resulting covariance matrix totally positive. Moreover, this reordering is identified and some cases for which the conditions for the covariance matrix of a multivariate Gaussian distribution to be totally positive are necessary and sufficient are provided.

Idioma: Inglés

DOI: 10.1016/j.cam.2023.115098

Año: 2023

Publicado en: Journal of Computational and Applied Mathematics 430 (2023), 115098[10 pp.]
ISSN: 0377-0427

Factor impacto JCR: 2.1 (2023)

Categ. JCR: MATHEMATICS, APPLIED rank: 53 / 332 = 0.16 (2023) - Q1 - T1

Factor impacto CITESCORE: 5.4 - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Factor impacto SCIMAGO: 0.858 - Computational Mathematics (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-20R
Financiación: info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/TIN2017-87600-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)