A direct sampler for G‐Wishart variates

Lenkoski, Alex

doi:10.1002/sta4.23

Cited by 54 publications

(75 citation statements)

References 25 publications

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“…Specifically, the proposed double Metropolis-Hastings approach relies on an approximation to the posterior and requires that moves in the graph space are constrained to edge-away neighbors. The recently proposed direct sampler of Lenkoski (2013), which resolves these limitations, could be considered as an alternative. In addition, although we have focused on normally distributed data, the approach can be extended to other types of graphical models, such as Ising or log-linear models.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Inference of Multiple Gaussian Graphical Models

Peterson

Stingo

Vannucci

2015

Journal of the American Statistical Association

159

207

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In this paper, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage similarity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We find improved accuracy of network estimation, particularly when the sample sizes within each subgroup are moderate. We also illustrate the application of our model to infer protein networks for various cancer subtypes and under different experimental conditions.

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Section: Discussionmentioning

confidence: 99%

Bayesian Inference of Multiple Gaussian Graphical Models

Peterson

Stingo

Vannucci

2015

Journal of the American Statistical Association

159

207

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“…Several sampling methods from the G-Wishart distribution have been proposed; to review existing methods see Wang and Li (2012). More recently, Lenkoski (2013) has developed an exact sampling algorithm for the G-Wishart distribution, borrowing an idea from Hastie, Tibshirani, and Friedman (2009). Algorithm 1 .…”

Section: Direct Sampler From G-wishartmentioning

confidence: 99%

BDgraph: An R Package for Bayesian Structure Learning in Graphical Models

Mohammadi¹,

Wit²

2019

J. Stat. Soft.

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Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce an R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decomposable) with continuous, discrete, and mixed variables. The package efficiently implements recent improvements in the Bayesian literature, including that of Mohammadi and Wit (2015) and Dobra and Mohammadi (2018). To speed up computations, the computationally intensive tasks have been implemented in C++ and interfaced with R, and the package has parallel computing capabilities. In addition, the package contains several functions for simulation and visualization, as well as several multivariate datasets taken from the literature and are used to describe the package capabilities. The paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. Furthermore, we illustrate the package's functionality in both real and artificial examples.

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“…[2011], Dobra & al. [2011], Wang & Li [2012], Lenkoski [2013], the more recent ones being generally more efficient than the preceding ones.…”

Section: Introductionmentioning

confidence: 96%

Bayesian precision and covariance matrix estimation for graphical Gaussian models with edge and vertex symmetries

Massam

Gao

2018

Biometrika

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Graphical Gaussian models with edge and vertex symmetries were introduced by Højsgaard & Lauritzen [2008] who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a Bayesian approach to the estimation of the precision matrix. We consider only those models where the symmetry constraints are imposed on the precision matrix and which thus form a natural exponential family with the precision matrix as the canonical parameter.We first identify the Diaconis-Ylvisaker conjugate prior for these models and develop a scheme to sample from the prior and posterior distributions. We thus obtain estimates of the posterior mean of the precision matrix.Second, in order to verify the precision of our estimate, we derive the explicit analytic expression of the expected value of the precision matrix when the graph underlying our model is a tree, a complete graph on three vertices and a decomposable graph on four vertices with various symmetries. In those cases, we compare our estimates with the exact value of the mean of the prior distribution. We also verify the accuracy of our estimates of the posterior mean on simulated data for graphs with up to thirty vertices and various symmetries.

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A direct sampler for G‐Wishart variates

Cited by 54 publications

References 25 publications

Bayesian Inference of Multiple Gaussian Graphical Models

Bayesian Inference of Multiple Gaussian Graphical Models

BDgraph: An R Package for Bayesian Structure Learning in Graphical Models

Bayesian precision and covariance matrix estimation for graphical Gaussian models with edge and vertex symmetries

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