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2021 Bayesian estimation of sparse precision matrices in the presence of Gaussian measurement error
Wenli Shi, Subhashis Ghosal, Ryan Martin
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Electron. J. Statist. 15(2): 4545-4579 (2021). DOI: 10.1214/21-EJS1904

Abstract

Estimation of sparse, high-dimensional precision matrices is an important and challenging problem. Existing methods all assume that observations can be made precisely but, in practice, this often is not the case; for example, the instruments used to measure the response may have limited precision. The present paper incorporates measurement error in the context of estimating a sparse, high-dimensional precision matrix. In particular, for a Gaussian graphical model with data corrupted by Gaussian measurement error with unknown variance, we establish a general result which gives sufficient conditions under which the posterior contraction rates that hold in the no-measurement-error case carry over to the measurement-error case. Interestingly, this result does not require that the measurement error variance be small. We apply our general result to several cases with well-known prior distributions for sparse precision matrices and also to a case with a newly-constructed prior for precision matrices with a sparse factor-loading form. Two different simulation studies highlight the empirical benefits of accounting for the measurement error as opposed to ignoring it, even when that measurement error is relatively small.

Funding Statement

S. Ghosal has been partially supported by Faculty Research and Professional Development Grant from the College of Sciences, North Carolina State University and Army Research Office grant 76643–MA. R. Martin has been partially supported by U.S. National Science Foundation grant DMS–1811802.

Citation

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Wenli Shi. Subhashis Ghosal. Ryan Martin. "Bayesian estimation of sparse precision matrices in the presence of Gaussian measurement error." Electron. J. Statist. 15 (2) 4545 - 4579, 2021. https://doi.org/10.1214/21-EJS1904

Information

Received: 1 December 2020; Published: 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.1214/21-EJS1904

Keywords: Gaussian graphical model , high-dimensional inference , measurement error , Posterior contraction rate , Sparsity

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Vol.15 • No. 2 • 2021
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