Total positivity in Markov structures
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....
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematical Statistics
2021
|
| Online Access: | https://hdl.handle.net/1721.1/133956 |
| _version_ | 1811088650349314048 |
|---|---|
| author | Fallat, Shaun Lauritzen, Steffen Sadeghi, Kayvan Uhler, Caroline Wermuth, Nanny Zwiernik, Piotr |
| author_facet | Fallat, Shaun Lauritzen, Steffen Sadeghi, Kayvan Uhler, Caroline Wermuth, Nanny Zwiernik, Piotr |
| author_sort | Fallat, Shaun |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:05:21Z |
| format | Article |
| id | mit-1721.1/133956 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:05:21Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1339562022-03-30T14:32:48Z Total positivity in Markov structures Fallat, Shaun Lauritzen, Steffen Sadeghi, Kayvan Uhler, Caroline Wermuth, Nanny Zwiernik, Piotr 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. 2021-10-27T19:57:22Z 2021-10-27T19:57:22Z 2017 2019-07-09T17:33:37Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133956 en 10.1214/16-AOS1478 The Annals of Statistics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Mathematical Statistics arXiv |
| spellingShingle | Fallat, Shaun Lauritzen, Steffen Sadeghi, Kayvan Uhler, Caroline Wermuth, Nanny Zwiernik, Piotr Total positivity in Markov structures |
| title | Total positivity in Markov structures |
| title_full | Total positivity in Markov structures |
| title_fullStr | Total positivity in Markov structures |
| title_full_unstemmed | Total positivity in Markov structures |
| title_short | Total positivity in Markov structures |
| title_sort | total positivity in markov structures |
| url | https://hdl.handle.net/1721.1/133956 |
| work_keys_str_mv | AT fallatshaun totalpositivityinmarkovstructures AT lauritzensteffen totalpositivityinmarkovstructures AT sadeghikayvan totalpositivityinmarkovstructures AT uhlercaroline totalpositivityinmarkovstructures AT wermuthnanny totalpositivityinmarkovstructures AT zwiernikpiotr totalpositivityinmarkovstructures |