Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Bayesian density estimation using Pitman-Yor or normalized
  inverse-Gaussian process kernel mixtures   We consider Bayesian nonparametric density estimation using a Pitman-Yor or a
normalized inverse-Gaussian process kernel mixture as the prior distribution
for a density. The procedure is studied from a frequentist perspective. Using
the stick-breaking representation of the Pitman-Yor process or the expression
of the finite-dimensional distributions for the normalized-inverse Gaussian
process, we prove that, when the data are replicates from an infinitely smooth
density, the posterior distribution concentrates on any shrinking $L^p$-norm
ball, $1\leq p\leq\infty$, around the sampling density at a \emph{nearly
parametric} rate, up to a logarithmic factor. The resulting hierarchical
Bayesian procedure, with a fixed prior, is thus shown to be adaptive to the
infinite degree of smoothness of the sampling density.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas