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Total positivity in Markov structures
Name
1510.01290.pdf
Description
Accepted version
Size
338.8 KB
Format
Adobe PDF
Checksum (MD5)
3bc087a2191406f26dc559bd1f6d4929
Author(s)
Fallat, Shaun
Lauritzen, Steffen
Sadeghi, Kayvan
Uhler, Caroline
Wermuth, Nanny
Zwiernik, Piotr
Date Issued
2017
Journal
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Version
Author's final manuscript
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.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1214/16-AOS1478
