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• W3204063022 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." @default.
• W3204063022 created "2021-10-11" @default.
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• W3204063022 date "2021-01-01" @default.
• W3204063022 modified "2023-09-27" @default.
• W3204063022 title "Bayesian estimation of sparse precision matrices in the presence of Gaussian measurement error" @default.
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• W3204063022 doi "https://doi.org/10.1214/21-ejs1904" @default.
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