Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Priors based on Splines with Random Knots   Splines are useful building blocks when constructing priors on nonparametric
models indexed by functions. Recently it has been established in the literature
that hierarchical priors based on splines with a random number of equally
spaced knots and random coefficients in the B-spline basis corresponding to
those knots lead, under certain conditions, to adaptive posterior contraction
rates, over certain smoothness functional classes. In this paper we extend
these results for when the location of the knots is also endowed with a prior.
This has already been a common practice in MCMC applications, where the
resulting posterior is expected to be more "spatially adaptive", but a
theoretical basis in terms of adaptive contraction rates was missing. Under
some mild assumptions, we establish a result that provides sufficient
conditions for adaptive contraction rates in a range of models.

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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con