--- _id: '1089' abstract: - lang: eng text: We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semigraphoid which is upward-stable and singleton-transitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2 distributions and discuss ways of constructing MTP2 distributions; in particular we give conditions on the log-linear parameters of a discrete distribution which ensure MTP2 and characterize conditional Gaussian distributions which satisfy MTP2. article_processing_charge: No author: - first_name: Shaun full_name: Fallat, Shaun last_name: Fallat - first_name: Steffen full_name: Lauritzen, Steffen last_name: Lauritzen - first_name: Kayvan full_name: Sadeghi, Kayvan last_name: Sadeghi - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Nanny full_name: Wermuth, Nanny last_name: Wermuth - first_name: Piotr full_name: Zwiernik, Piotr last_name: Zwiernik citation: ama: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. Total positivity in Markov structures. Annals of Statistics. 2017;45(3):1152-1184. doi:10.1214/16-AOS1478 apa: Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., & Zwiernik, P. (2017). Total positivity in Markov structures. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AOS1478 chicago: Fallat, Shaun, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, and Piotr Zwiernik. “Total Positivity in Markov Structures.” Annals of Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AOS1478. ieee: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, and P. Zwiernik, “Total positivity in Markov structures,” Annals of Statistics, vol. 45, no. 3. Institute of Mathematical Statistics, pp. 1152–1184, 2017. ista: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. 2017. Total positivity in Markov structures. Annals of Statistics. 45(3), 1152–1184. mla: Fallat, Shaun, et al. “Total Positivity in Markov Structures.” Annals of Statistics, vol. 45, no. 3, Institute of Mathematical Statistics, 2017, pp. 1152–84, doi:10.1214/16-AOS1478. short: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, P. Zwiernik, Annals of Statistics 45 (2017) 1152–1184. date_created: 2018-12-11T11:50:05Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T11:46:53Z day: '01' department: - _id: CaUh doi: 10.1214/16-AOS1478 external_id: isi: - '000404395900008' intvolume: ' 45' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1510.01290 month: '06' oa: 1 oa_version: Submitted Version page: 1152 - 1184 project: - _id: 2530CA10-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Y 903-N35 name: 'Gaussian Graphical Models: Theory and Applications' publication: Annals of Statistics publication_identifier: issn: - '00905364' publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6288' quality_controlled: '1' scopus_import: '1' status: public title: Total positivity in Markov structures type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 45 year: '2017' ...