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MODEL SELECTION IN THE SPACE OF GAUSSIAN MODELS INVARIANT BY SYMMETRY

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02564982
Contributor : Piotr Graczyk <>
Submitted on : Wednesday, May 6, 2020 - 10:02:17 AM
Last modification on : Saturday, May 16, 2020 - 3:35:57 AM

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

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