Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cross Validated Non parametric Bayesianism by Markov Chain Monte Carlo   Completely automatic and adaptive non-parametric inference is a pie in the
sky. The frequentist approach, best exemplified by the kernel estimators, has
excellent asymptotic characteristics but it is very sensitive to the choice of
smoothness parameters. On the other hand the Bayesian approach, best
exemplified by the mixture of gaussians models, is optimal given the observed
data but it is very sensitive to the choice of prior. In 1984 the author
proposed to use the Cross-Validated gaussian kernel as the likelihood for the
smoothness scale parameter h, and obtained a closed formula for the posterior
mean of h based on Jeffreys's rule as the prior. The practical operational
characteristics of this bayes' rule for the smoothness parameter remained
unknown for all these years due to the combinatorial complexity of the formula.
It is shown in this paper that a version of the metropolis algorithm can be
used to approximate the value of h producing remarkably good completely
automatic and adaptive kernel estimators. A close study of the form of the
cross validated likelihood suggests a modification and a new approach to
Bayesian Non-parametrics in general.

2
The categories of this paper are: math
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th