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.
Binary Variables
Distributions
faithfulness
Matrices
Association
concentration graph
graphical models
Graphical Models
Dependence
Association
conditional Gaussian distribution
Conditional-Independence
Correlation Inequalities
Författare
S. Fallat
University of Regina
S. Lauritzen
Köpenhamns universitet
K. Sadeghi
University of Cambridge
C. Uhler
Massachusetts Institute of Technology (MIT)
Institute of Science and Technology Austria
Nanny Wermuth
Göteborgs universitet
Chalmers, Matematiska vetenskaper
P. Zwiernik
Barcelona Graduate School of Economics
Annals of Statistics
0090-5364 (ISSN)
Vol. 45 3 1152-1184Ämneskategorier
Matematik
Infrastrukturteknik
DOI
10.1214/16-AOS1478