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A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

We consider a class of colored graphical Gaussian models obtained by placing symmetry constraints on the precision matrix in a Bayesian framework. The prior distribution on the precision matrix is the colored $G$-Wishart prior which is the…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…