Open Access
November 2005 Experiments in Stochastic Computation for High-Dimensional Graphical Models
Beatrix Jones, Carlos Carvalho, Adrian Dobra, Chris Hans, Chris Carter, Mike West
Statist. Sci. 20(4): 388-400 (November 2005). DOI: 10.1214/088342305000000304


We discuss the implementation, development and performance of methods of stochastic computation in Gaussian graphical models. We view these methods from the perspective of high-dimensional model search, with a particular interest in the scalability with dimension of Markov chain Monte Carlo (MCMC) and other stochastic search methods. After reviewing the structure and context of undirected Gaussian graphical models and model uncertainty (covariance selection), we discuss prior specifications, including new priors over models, and then explore a number of examples using various methods of stochastic computation. Traditional MCMC methods are the point of departure for this experimentation; we then develop alternative stochastic search ideas and contrast this new approach with MCMC. Our examples range from low (12–20) to moderate (150) dimension, and combine simple synthetic examples with data analysis from gene expression studies. We conclude with comments about the need and potential for new computational methods in far higher dimensions, including constructive approaches to Gaussian graphical modeling and computation.


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Beatrix Jones. Carlos Carvalho. Adrian Dobra. Chris Hans. Chris Carter. Mike West. "Experiments in Stochastic Computation for High-Dimensional Graphical Models." Statist. Sci. 20 (4) 388 - 400, November 2005.


Published: November 2005
First available in Project Euclid: 12 January 2006

zbMATH: 1130.62408
MathSciNet: MR2210226
Digital Object Identifier: 10.1214/088342305000000304

Keywords: decomposable models , Markov chain Monte Carlo , nondecomposable models , parallel implementation , shotgun stochastic search

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.20 • No. 4 • November 2005
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