Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ultra High-dimensional Multivariate Posterior Contraction Rate Under
  Shrinkage Priors   In recent years, shrinkage priors have received much attention in
high-dimensional data analysis from a Bayesian perspective. Compared with
widely used spike-and-slab priors, shrinkage priors have better computational
efficiency. But the theoretical properties, especially posterior contraction
rate, which is important in uncertainty quantification, are not established in
many cases. In this paper, we apply global-local shrinkage priors to
high-dimensional multivariate linear regression with unknown covariance matrix.
We show that when the prior is highly concentrated near zero and has heavy
tail, the posterior contraction rates for both coefficients matrix and
covariance matrix are nearly optimal. Our results hold when number of features
p grows much faster than the sample size n, which is of great interest in
modern data analysis. We show that a class of readily implementable scale
mixture of normal priors satisfies the conditions of the main theorem.

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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph