Bernstein-von Mises Theorems for Functionals of Covariance Matrix
Statistics Theory
2014-12-02 v1 Statistics Theory
Abstract
We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including entries of covariance matrix, entries of precision matrix, quadratic forms, log-determinant, eigenvalues in the Bayesian Gaussian covariance/precision matrix estimation setting, as well as for Bayesian linear and quadratic discriminant analysis.
Keywords
Cite
@article{arxiv.1412.0313,
title = {Bernstein-von Mises Theorems for Functionals of Covariance Matrix},
author = {Chao Gao and Harrison H. Zhou},
journal= {arXiv preprint arXiv:1412.0313},
year = {2014}
}