Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correct estimate of the probability of false detection of the matched
  filter in weak-signal detection problems. III (Peak distribution method
  versus the Gumbel distribution method)   The matched filter (MF) represents one of the main tools to detect signals
from known sources embedded in the noise. In the Gaussian case the noise is
assumed to be the realization of a Gaussian random field (GRF). The most
important property of the MF, the maximization of the probability of detection
subject to a constant probability of false detection or false alarm (PFA),
makes it one of the most popular techniques. However, the MF technique relies
upon the a priori knowledge of the number and the position of the searched
signals in the GRF which usually are not available. A typical way out is to
assume that the position of a signal coincides with one of the peaks in the
matched filtered data. A detection is claimed when the probability that a given
peak is due only to the noise (i.e. the PFA) is smaller than a prefixed
threshold. In this case the probability density function (PDF) of the
amplitudes has to be used for the computation of the PFA, which is different
from the Gaussian. Moreover, the probability that a detection is false depends
on the number of peaks present in the filtered GRF, the greater the number of
peaks in a GRF, the higher the probability of peaks due to the noise that
exceed the detection threshold. If not taken into account, the PFA can be
severely underestimated. Many solutions proposed to this problem are
non-parametric hence not able to exploit all the available information. This
limitation has been overcome by means of two efficient parametric approaches,
one based on the PDF of the peak amplitudes of a smooth and isotropic GRF
whereas the other uses the Gumbel distribution (the asymptotic PDF of the
corresponding extreme). Simulations and ALMA maps show that, although the two
methods produce almost identical results, the first is more flexible and allows
us to check the reliability of the detection procedure.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org