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Posterior convergence rates for high‐dimensional precision matrix estimation using G ‐Wishart priors
Author(s) -
Banerjee Sayantan
Publication year - 2017
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.147
Subject(s) - wishart distribution , cholesky decomposition , prior probability , mathematics , convergence (economics) , matrix (chemical analysis) , rate of convergence , gaussian , posterior probability , graphical model , algorithm , extension (predicate logic) , computer science , bayesian probability , statistics , multivariate statistics , eigenvalues and eigenvectors , computer network , channel (broadcasting) , physics , materials science , quantum mechanics , economics , composite material , economic growth , programming language
We study the posterior convergence behaviour of a precision matrix corresponding to a Gaussian graphical model in the high‐dimensional set‐up under sparsity assumptions. Recent works include studying posterior convergence rates of precision matrices assuming an approximate banding structure, and extension of such result to arbitrary decomposable graphical models using a transformation to Cholesky factor of the precision matrices. In this paper, we study the same for the wider class of arbitrary decomposable graphical models under similar sparsity assumptions using a G ‐Wishart prior, but without the complications of using a Cholesky factor, and arrive at identical posterior convergence rates. Copyright © 2017 John Wiley & Sons, Ltd.