Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyper-differential sensitivity analysis for nonlinear Bayesian inverse
  problems   We consider hyper-differential sensitivity analysis (HDSA) of nonlinear
Bayesian inverse problems governed by PDEs with infinite-dimensional
parameters. In previous works, HDSA has been used to assess the sensitivity of
the solution of deterministic inverse problems to additional model
uncertainties and also different types of measurement data. In the present
work, we extend HDSA to the class of Bayesian inverse problems governed by
PDEs. The focus is on assessing the sensitivity of certain key quantities
derived from the posterior distribution. Specifically, we focus on analyzing
the sensitivity of the MAP point and the Bayes risk and make full use of the
information embedded in the Bayesian inverse problem. After establishing our
mathematical framework for HDSA of Bayesian inverse problems, we present a
detailed computational approach for computing the proposed HDSA indices. We
examine the effectiveness of the proposed approach on a model inverse problem
governed by a PDE for heat conduction.

0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int