Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse Deterministic Approximation of Bayesian Inverse Problems   We present a parametric deterministic formulation of Bayesian inverse
problems with input parameter from infinite dimensional, separable Banach
spaces. In this formulation, the forward problems are parametric, deterministic
elliptic partial differential equations, and the inverse problem is to
determine the unknown, parametric deterministic coefficients from noisy
observations comprising linear functionals of the solution.
  We prove a generalized polynomial chaos representation of the posterior
density with respect to the prior measure, given noisy observational data. We
analyze the sparsity of the posterior density in terms of the summability of
the input data's coefficient sequence. To this end, we estimate the
fluctuations in the prior. We exhibit sufficient conditions on the prior model
in order for approximations of the posterior density to converge at a given
algebraic rate, in terms of the number $N$ of unknowns appearing in the
parameteric representation of the prior measure. Similar sparsity and
approximation results are also exhibited for the solution and covariance of the
elliptic partial differential equation under the posterior. These results then
form the basis for efficient uncertainty quantification, in the presence of
data with noise.

4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph