Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized statistics: applications to data inverse problems with
  outlier-resistance   The conventional approach to data-driven inversion framework is based on
Gaussian statistics that presents serious difficulties, especially in the
presence of outliers in the measurements. In this work, we present maximum
likelihood estimators associated with generalized Gaussian distributions in the
context of R\'enyi, Tsallis and Kaniadakis statistics. In this regard, we
analytically analyse the outlier-resistance of each proposal through the
so-called influence function. In this way, we formulate inverse problems by
constructing objective functions linked to the maximum likelihood estimators.
To demonstrate the robustness of the generalized methodologies, we consider an
important geophysical inverse problem with high noisy data with spikes. The
results reveal that the best data inversion performance occurs when the
entropic index from each generalized statistic is associated with objective
functions proportional to the inverse of the error amplitude. We argue that in
such a limit the three approaches are resistant to outliers and are also
equivalent, which suggests a lower computational cost for the inversion process
due to the reduction of numerical simulations to be performed and the fast
convergence of the optimization process.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int