Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple integral representation for functionals of Dirichlet processes   We point out that a proper use of the Hoeffding--ANOVA decomposition for
symmetric statistics of finite urn sequences, previously introduced by the
author, yields a decomposition of the space of square-integrable functionals of
a Dirichlet--Ferguson process, written $L^2(D)$, into orthogonal subspaces of
multiple integrals of increasing order. This gives an isomorphism between
$L^2(D)$ and an appropriate Fock space over a class of deterministic functions.
By means of a well-known result due to Blackwell and MacQueen, we show that
each element of the $n$th orthogonal space of multiple integrals can be
represented as the $L^2$ limit of $U$-statistics with degenerate kernel of
degree $n$. General formulae for the decomposition of a given functional are
provided in terms of linear combinations of conditioned expectations whose
coefficients are explicitly computed. We show that, in simple cases, multiple
integrals have a natural representation in terms of Jacobi polynomials. Several
connections are established, in particular with Bayesian decision problems, and
with some classic formulae concerning the transition densities of multiallele
diffusion models, due to Littler and Fackerell, and Griffiths. Our results may
also be used to calculate the best approximation of elements of $L^2(D)$ by
means of $U$-statistics of finite vectors of exchangeable observations.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org