Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical dependence: Beyond Pearson's $\rho$   Pearson's $\rho$ is the most used measure of statistical dependence. It gives
a complete characterization of dependence in the Gaussian case, and it also
works well in some non-Gaussian situations. It is well known, however, that it
has a number of shortcomings; in particular for heavy tailed distributions and
in nonlinear situations, where it may produce misleading, and even disastrous
results. In recent years a number of alternatives have been proposed. In this
paper, we will survey these developments, especially results obtained in the
last couple of decades. Among measures discussed are the copula,
distribution-based measures, the distance covariance, the HSIC measure popular
in machine learning, and finally the local Gaussian correlation, which is a
local version of Pearson's $\rho$. Throughout we put the emphasis on conceptual
developments and a comparison of these. We point out relevant references to
technical details as well as comparative empirical and simulated experiments.
There is a broad selection of references under each topic treated.

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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: econ