## Electronic Journal of Statistics

### High dimensional posterior convergence rates for decomposable graphical models

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2828-2854.

Dates
First available in Project Euclid: 31 December 2015

https://projecteuclid.org/euclid.ejs/1451577218

Digital Object Identifier
doi:10.1214/15-EJS1084

Mathematical Reviews number (MathSciNet)
MR3439186

Zentralblatt MATH identifier
1329.62152

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62G20: Asymptotic properties

#### Citation

Xiang, Ruoxuan; Khare, Kshitij; Ghosh, Malay. High dimensional posterior convergence rates for decomposable graphical models. Electron. J. Statist. 9 (2015), no. 2, 2828--2854. doi:10.1214/15-EJS1084. https://projecteuclid.org/euclid.ejs/1451577218

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