Fallat, S;
Lauritzen, S;
Sadeghi, K;
Uhler, C;
Wermuth, N;
Zwiernik, P;
(2017)
Total positivity in Markov structures.
The Annals of Statistics
, 45
(3)
pp. 1152-1184.
10.1214/16-AOS1478.
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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 singleton-transitive. 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.
| Type: | Article |
|---|---|
| Title: | Total positivity in Markov structures |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/16-AOS1478 |
| Publisher version: | https://doi.org/10.1214/16-AOS1478 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10058843 |
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