Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Certified dimension reduction in nonlinear Bayesian inverse problems   We propose a dimension reduction technique for Bayesian inverse problems with
nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation
noise. The likelihood function is approximated by a ridge function, i.e., a map
which depends non-trivially only on a few linear combinations of the
parameters. We build this ridge approximation by minimizing an upper bound on
the Kullback--Leibler divergence between the posterior distribution and its
approximation. This bound, obtained via logarithmic Sobolev inequalities,
allows one to certify the error of the posterior approximation. Computing the
bound requires computing the second moment matrix of the gradient of the
log-likelihood function. In practice, a sample-based approximation of the upper
bound is then required. We provide an analysis that enables control of the
posterior approximation error due to this sampling. Numerical and theoretical
comparisons with existing methods illustrate the benefits of the proposed
methodology.

25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat