---
_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'
...