Total Positivity In Markov Structures
Journal article, 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
Author
S. Fallat
University of Regina
S. Lauritzen
University of Copenhagen
K. Sadeghi
University of Cambridge
C. Uhler
Massachusetts Institute of Technology (MIT)
Institute of Science and Technology Austria
Nanny Wermuth
Chalmers, Mathematical Sciences
University of Gothenburg
P. Zwiernik
Barcelona Graduate School of Economics
Annals of Statistics
0090-5364 (ISSN)
Vol. 45 3 1152-1184Subject Categories
Mathematics
DOI
10.1214/16-AOS1478