Total Positivity In Markov Structures
Artikel i vetenskaplig tidskrift, 2017

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.

Correlation Inequalities

Conditional-Independence

concentration graph

Association

faithfulness

Matrices

Dependence

Distributions

Association

Binary Variables

conditional Gaussian distribution

graphical models

Graphical Models

Författare

S. Fallat

University of Regina

S. Lauritzen

Köbenhavns Universitet

K. Sadeghi

University of Cambridge

C. Uhler

Massachusetts Institute of Technology (MIT)

Institute of Science and Technology Austria

Nanny Wermuth

Chalmers, Matematiska vetenskaper

Göteborgs universitet

P. Zwiernik

Barcelona Graduate School of Economics

Annals of Statistics

0090-5364 (ISSN)

Vol. 45 3 1152-1184

Ämneskategorier

Matematik

DOI

10.1214/16-AOS1478