000126870 001__ 126870 000126870 005__ 20241125101155.0 000126870 0247_ $$2doi$$a10.1016/j.cam.2023.115098 000126870 0248_ $$2sideral$$a134129 000126870 037__ $$aART-2023-134129 000126870 041__ $$aeng 000126870 100__ $$aBaz, Juan 000126870 245__ $$aGaussian Markov Random fields and totally positive matrices 000126870 260__ $$c2023 000126870 5060_ $$aAccess copy available to the general public$$fUnrestricted 000126870 5203_ $$aThe 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. 000126870 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-20R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/TIN2017-87600-P 000126870 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000126870 590__ $$a2.1$$b2023 000126870 592__ $$a0.858$$b2023 000126870 591__ $$aMATHEMATICS, APPLIED$$b53 / 332 = 0.16$$c2023$$dQ1$$eT1 000126870 593__ $$aComputational Mathematics$$c2023$$dQ2 000126870 593__ $$aApplied Mathematics$$c2023$$dQ2 000126870 594__ $$a5.4$$b2023 000126870 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000126870 700__ $$aAlonso, Pedro 000126870 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, Juan Manuel$$uUniversidad de Zaragoza 000126870 700__ $$aPérez-Fernández, Raúl 000126870 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000126870 773__ $$g430 (2023), 115098[10 pp.]$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427 000126870 8564_ $$s399422$$uhttps://zaguan.unizar.es/record/126870/files/texto_completo.pdf$$yVersión publicada 000126870 8564_ $$s2321431$$uhttps://zaguan.unizar.es/record/126870/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000126870 909CO $$ooai:zaguan.unizar.es:126870$$particulos$$pdriver 000126870 951__ $$a2024-11-22-12:08:51 000126870 980__ $$aARTICLE