Total Positivity in Markov Structures

Shaun Fallat; Steffen L. Lauritzen; Kayvan Sadeghi; Caroline Uhler; Nanny Wermuth; Piotr Zwiernik

doi:10.1214/16-aos1478

Total Positivity in Markov Structures

Shaun Fallat, Steffen L. Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, Piotr Zwiernik

Institut for Matematiske Fag

16 Citationer (Scopus)

Abstract

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 semi-graphoid which is upward-stable and singletontransitive. 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.

Originalsprog	Engelsk
Tidsskrift	Annals of Statistics
Vol/bind	45
Udgave nummer	3
Sider (fra-til)	1152-1184
ISSN	0090-5364
DOI	https://doi.org/10.1214/16-aos1478
Status	Udgivet - jun. 2017

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10.1214/16-aos1478

http://web.math.ku.dk/~lauritzen/papers/AOS1478.pdfLicens: Andet

Citationsformater

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abstract = "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 semi-graphoid which is upward-stable and singletontransitive. 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.",

author = "Shaun Fallat and Lauritzen, {Steffen L.} and Kayvan Sadeghi and Caroline Uhler and Nanny Wermuth and Piotr Zwiernik",

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language = "English",

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TY - JOUR

T1 - Total Positivity in Markov Structures

AU - Fallat, Shaun

AU - Lauritzen, Steffen L.

AU - Sadeghi, Kayvan

AU - Uhler, Caroline

AU - Wermuth, Nanny

AU - Zwiernik, Piotr

PY - 2017/6

Y1 - 2017/6

N2 - 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 semi-graphoid which is upward-stable and singletontransitive. 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.

AB - 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 semi-graphoid which is upward-stable and singletontransitive. 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.

U2 - 10.1214/16-aos1478

DO - 10.1214/16-aos1478

M3 - Journal article

SN - 0090-5364

VL - 45

SP - 1152

EP - 1184

JO - Annals of Statistics

JF - Annals of Statistics

IS - 3

ER -

Total Positivity in Markov Structures

Abstract

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