Electronic Journal of Statistics

Efficient Gaussian graphical model determination under G-Wishart prior distributions

Hao Wang and Sophia Zhengzi Li

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Abstract

This paper proposes a new algorithm for Bayesian model determination in Gaussian graphical models under G-Wishart prior distributions. We first review recent development in sampling from G-Wishart distributions for given graphs, with a particular interest in the efficiency of the block Gibbs samplers and other competing methods. We generalize the maximum clique block Gibbs samplers to a class of flexible block Gibbs samplers and prove its convergence. This class of block Gibbs samplers substantially outperforms its competitors along a variety of dimensions. We next develop the theory and computational details of a novel Markov chain Monte Carlo sampling scheme for Gaussian graphical model determination. Our method relies on the partial analytic structure of G-Wishart distributions integrated with the exchange algorithm. Unlike existing methods, the new method requires neither proposal tuning nor evaluation of normalizing constants of G-Wishart distributions.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 168-198.

Dates
First available in Project Euclid: 3 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1328280902

Digital Object Identifier
doi:10.1214/12-EJS669

Mathematical Reviews number (MathSciNet)
MR2879676

Zentralblatt MATH identifier
1335.62069

Keywords
Exchange algorithms Gaussian graphical models G-Wishart hyper-inverse Wishart Gibbs sampler non-decomposable graphs partial analytic structure posterior simulation

Citation

Wang, Hao; Li, Sophia Zhengzi. Efficient Gaussian graphical model determination under G -Wishart prior distributions. Electron. J. Statist. 6 (2012), 168--198. doi:10.1214/12-EJS669. https://projecteuclid.org/euclid.ejs/1328280902


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