The <i>G</i>-Wishart Weighted Proposal Algorithm: Efficient Posterior Computation for Gaussian Graphical Models

Efficient Gaussian graphical model determination under G-Wishart prior distributions

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 o...

Efficient Computation of `1 Regularized Estimates in Gaussian Graphical Models

In this article, I propose an efficient algorithm to compute `1 regularized maximum likelihood estimates in the Gaussian graphical model. These estimators, recently proposed in an earlier article by Yuan and Lin, conduct parameter estimation and model selection simultaneously and have been shown to enjoy nice properties in both large and finite samples. To compute the estimates, however, can be...

Efficient Neighborhood Selection for Gaussian Graphical Models

This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both algorithms are shown to be structurally consistent, and efficient. Numerical res...

Efficient Gradient Computation for Conditional Gaussian Models

Computational Aspects Related to Inference in Gaussian Graphical Models With the G-Wishart Prior

We describe a comprehensive framework for performing Bayesian inference for Gaussian graphical models based on the G-Wishart prior with a special focus on efficiently including nondecomposable graphs in the model space. We develop a new approximation method to the normalizing constant of a G-Wishart distribution based on the Laplace approximation. We review recent developments in stochastic sea...