Abstract
Gaussian concentration graphical models are one of the most popular models for sparse covariance estimation with high-dimensional data. In recent years, much research has gone into development of methods which facilitate Bayesian inference for these models under the standard $G$-Wishart prior. However, convergence properties of the resulting posteriors are not completely understood, particularly in high-dimensional settings. In this paper, we derive high-dimensional posterior convergence rates for the class of decomposable concentration graphical models. A key initial step which facilitates our analysis is transformation to the Cholesky factor of the inverse covariance matrix. As a by-product of our analysis, we also obtain convergence rates for the corresponding maximum likelihood estimator.
Citation
Ruoxuan Xiang. Kshitij Khare. Malay Ghosh. "High dimensional posterior convergence rates for decomposable graphical models." Electron. J. Statist. 9 (2) 2828 - 2854, 2015. https://doi.org/10.1214/15-EJS1084
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