Bernstein-von Mises Theorems for Functionals of Covariance Matrix

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.

References in corpus (4)

• Sparse principal component analysis and iterative thresholding
• On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
• Law of Log Determinant of Sample Covariance Matrix and Optimal Estimation of Differential Entropy for High-Dimensional Gaussian Distributions
• Adaptive Bernstein-von Mises theorems in Gaussian white noise