---
_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. <i>Annals of Statistics</i>. 2017;45(3):1152-1184. doi:<a
    href="https://doi.org/10.1214/16-AOS1478">10.1214/16-AOS1478</a>
  apa: Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., &#38; Zwiernik,
    P. (2017). Total positivity in Markov structures. <i>Annals of Statistics</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/16-AOS1478">https://doi.org/10.1214/16-AOS1478</a>
  chicago: Fallat, Shaun, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny
    Wermuth, and Piotr Zwiernik. “Total Positivity in Markov Structures.” <i>Annals
    of Statistics</i>. Institute of Mathematical Statistics, 2017. <a href="https://doi.org/10.1214/16-AOS1478">https://doi.org/10.1214/16-AOS1478</a>.
  ieee: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, and P. Zwiernik,
    “Total positivity in Markov structures,” <i>Annals of Statistics</i>, 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.” <i>Annals of
    Statistics</i>, vol. 45, no. 3, Institute of Mathematical Statistics, 2017, pp.
    1152–84, doi:<a href="https://doi.org/10.1214/16-AOS1478">10.1214/16-AOS1478</a>.
  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'
...