  The matched filter (MF) is one of the most popular and reliable techniques to
the detect signals of known structure and amplitude smaller than the level of
the contaminating noise. Under the assumption of stationary Gaussian noise, MF
maximizes the probability of detection subject to a constant probability of
false detection or false alarm (PFA). This property relies upon a priori
knowledge of the position of the searched signals, which is usually not
available. Recently, it has been shown that when applied in its standard form,
MF may severely underestimate the PFA. As a consequence the statistical
significance of features that belong to noise is overestimated and the
resulting detections are actually spurious. For this reason, an alternative
method of computing the PFA has been proposed that is based on the probability
density function (PDF) of the peaks of an isotropic Gaussian random field. In
this paper we further develop this method. In particular, we discuss the
statistical meaning of the PFA and show that, although useful as a preliminary
step in a detection procedure, it is not able to quantify the actual
reliability of a specific detection. For this reason, a new quantity is
introduced called the specific probability of false alarm (SPFA), which is able
to carry out this computation. We show how this method works in targeted
simulations and apply it to a few interferometric maps taken with the Atacama
Large Millimeter/submillimeter Array (ALMA) and the Australia Telescope Compact
Array (ATCA). We select a few potential new point sources and assign an
accurate detection reliability to these sources.
