Geodesic
On Gaussian conditional independence structures
Kybernetika, Tome 43 (2007) no. 3, pp. 327-342

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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.
Classification : 15A15, 60E05
Keywords: multivariate Gaussian distribution; positive definite matrices; determinants; principal minors; conditional independence; probabilistic representability; semigraphoids; separation graphoids; gaussoids; covariance selection models; Markov perfectness 
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     author = {Ln\v{e}ni\v{c}ka, Radim and Mat\'u\v{s}, Franti\v{s}ek},
     title = {On {Gaussian} conditional independence structures},
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     pages = {327--342},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2007},
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     zbl = {1144.60302},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_3_a4/}
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Lněnička, Radim; Matúš, František. On Gaussian conditional independence structures. Kybernetika, Tome 43 (2007) no. 3, pp. 327-342. http://geodesic.mathdoc.fr/item/KYB_2007__43_3_a4/