Model selection in the space of Gaussian models invariant by symmetry
具有对称不变性的高斯模型空间中的模型选择
We consider multivariate centered 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…