Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posterior concentration rates for empirical Bayes procedures, with
  applications to Dirichlet Process mixtures   In this paper we provide general conditions to check on the model and the
prior to derive posterior concentration rates for data-dependent priors (or
empirical Bayes approaches). We aim at providing conditions that are close to
the conditions provided in the seminal paper by Ghosal and van der Vaart
(2007a). We then apply the general theorem to two different settings: the
estimation of a density using Dirichlet process mixtures of Gaussian random
variables with base measure depending on some empirical quantities and the
estimation of the intensity of a counting process under the Aalen model. A
simulation study for inhomogeneous Poisson processes also illustrates our
results. In the former case we also derive some results on the estimation of
the mixing density and on the deconvolution problem. In the latter, we provide
a general theorem on posterior concentration rates for counting processes with
Aalen multiplicative intensity with priors not depending on the data.

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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph