Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An adaptive kriging method for solving nonlinear inverse statistical
  problems   In various industrial contexts, estimating the distribution of unobserved
random vectors Xi from some noisy indirect observations H(Xi) + Ui is required.
If the relation between Xi and the quantity H(Xi), measured with the error Ui,
is implemented by a CPU-consuming computer model H, a major practical
difficulty is to perform the statistical inference with a relatively small
number of runs of H. Following Fu et al. (2014), a Bayesian statistical
framework is considered to make use of possible prior knowledge on the
parameters of the distribution of the Xi, which is assumed Gaussian. Moreover,
a Markov Chain Monte Carlo (MCMC) algorithm is carried out to estimate their
posterior distribution by replacing H by a kriging metamodel build from a
limited number of simulated experiments. Two heuristics, involving two
different criteria to be optimized, are proposed to sequentially design these
computer experiments in the limits of a given computational budget. The first
criterion is a Weighted Integrated Mean Square Error (WIMSE). The second one,
called Expected Conditional Divergence (ECD), developed in the spirit of the
Stepwise Uncertainty Reduction (SUR) criterion, is based on the discrepancy
between two consecutive approximations of the target posterior distribution.
Several numerical comparisons conducted over a toy example then a motivating
real case-study show that such adaptive designs can significantly outperform
the classical choice of a maximin Latin Hypercube Design (LHD) of experiments.
Dealing with a major concern in hydraulic engineering, a particular emphasis is
placed upon the prior elicitation of the case-study, highlighting the overall
feasibility of the methodology. Faster convergences and manageability
considerations lead to recommend the use of the ECD criterion in practical
applications.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int