On Gaussian conditional independence structures

Radim Lněnička; František Matúš

Kybernetika (2007)

  • Volume: 43, Issue: 3, page 327-342
  • ISSN: 0023-5954

Abstract

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The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.

How to cite

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Lněnička, Radim, and Matúš, František. "On Gaussian conditional independence structures." Kybernetika 43.3 (2007): 327-342. <http://eudml.org/doc/33861>.

@article{Lněnička2007,
abstract = {The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.},
author = {Lněnička, Radim, Matúš, František},
journal = {Kybernetika},
keywords = {multivariate Gaussian distribution; positive definite matrices; determinants; principal minors; conditional independence; probabilistic representability; semigraphoids; separation graphoids; gaussoids; covariance selection models; Markov perfectness; multivariate Gaussian distribution; separation graphoids; gaussoids; covariance selection models; Markov perfectness},
language = {eng},
number = {3},
pages = {327-342},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On Gaussian conditional independence structures},
url = {http://eudml.org/doc/33861},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Lněnička, Radim
AU - Matúš, František
TI - On Gaussian conditional independence structures
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 3
SP - 327
EP - 342
AB - The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.
LA - eng
KW - multivariate Gaussian distribution; positive definite matrices; determinants; principal minors; conditional independence; probabilistic representability; semigraphoids; separation graphoids; gaussoids; covariance selection models; Markov perfectness; multivariate Gaussian distribution; separation graphoids; gaussoids; covariance selection models; Markov perfectness
UR - http://eudml.org/doc/33861
ER -

References

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