Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The statistical finite element method (statFEM) for coherent synthesis
  of observation data and model predictions   The increased availability of observation data from engineering systems in
operation poses the question of how to incorporate this data into finite
element models. To this end, we propose a novel statistical construction of the
finite element method that provides the means of synthesising measurement data
and finite element models. The Bayesian statistical framework is adopted to
treat all the uncertainties present in the data, the mathematical model and its
finite element discretisation. From the outset, we postulate a data-generating
model which additively decomposes data into a finite element, a model
misspecification and a noise component. Each of the components may be uncertain
and is considered as a random variable with a respective prior probability
density. The prior of the finite element component is given by a conventional
stochastic forward problem. The prior probabilities of the model
misspecification and measurement noise, without loss of generality, are assumed
to have zero-mean and known covariance structure. Our proposed statistical
model is hierarchical in the sense that each of the three random components may
depend on non-observable random hyperparameters. Because of the hierarchical
structure of the statistical model, Bayes rule is applied on three different
levels in turn to infer the posterior densities of the three random components
and hyperparameters. On level one, we determine the posterior densities of the
finite element component and the true system response using the prior finite
element density given by the forward problem and the data likelihood. On the
next level, we infer the hyperparameter posterior densities from their
respective priors and the marginal likelihood of the first inference problem.
Finally, on level three we use Bayes rule to choose the most suitable finite
element model in light of the observed data by computing the model posteriors.

7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an