MODEL SELECTION IN THE SPACE OF GAUSSIAN MODELS INVARIANT BY SYMMETRY - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

MODEL SELECTION IN THE SPACE OF GAUSSIAN MODELS INVARIANT BY SYMMETRY

Bartosz Kołodziejek
  • Fonction : Auteur
  • PersonId : 1069227

Résumé

We consider multivariate centred Gaussian models for the random variable Z = (Z1,. .. , Zp), invariant under the action of a subgroup of the group of permutations on {1,. .. , p}. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter Σ and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter K = Σ ^{−1}. We can thus perform Bayesian model selection in the class of complete Gaussian models invariant by the action of a subgroup of the symmetric group, which we could also call complete RCOP models. We illustrate our results with a toy example of dimension 4 and several examples for selection within cyclic groups, including a high dimensional example with p = 100.
Fichier principal
Vignette du fichier
GIKM.pdf (531.82 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02564982 , version 1 (06-05-2020)

Identifiants

  • HAL Id : hal-02564982 , version 1

Citer

Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek, Helene Massam. MODEL SELECTION IN THE SPACE OF GAUSSIAN MODELS INVARIANT BY SYMMETRY. 2020. ⟨hal-02564982⟩
33 Consultations
49 Téléchargements

Partager

Gmail Facebook X LinkedIn More