TOTAL POSITIVITY IN MARKOV STRUCTURES

• 成果类型: Article
• 署名作者: Fallat, Shaun; Lauritzen, Steffen; Sadeghi, Kayvan; Uhler, Caroline; Wermuth, Nanny; Zwiernik, Piotr
• 署名单位: University of Regina; University of Copenhagen; University of Cambridge; Massachusetts Institute of Technology (MIT); Institute of Science & Technology - Austria; Chalmers University of Technology; Johannes Gutenberg University of Mainz; Pompeu Fabra University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1478
• 发表日期: 2017
• 页码: 1152-1184
• 关键词: conditional-independence; correlation inequalities; association; matrices; models

摘要

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.