The correct estimate of the probability of false detection of the matched filter in the detection of weak signals. II. (Further results with application to a set of ALMA and ATCA data)

Abstract

The matched filter (MF) is one of the most popular and reliable technique for the detection of 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 a detection for a fixed 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. In a recent work, Vio and Andreani (2016, A&A, 589, A20) have 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, the same authors present an alternative method of computing the PFA which 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, say the 'specific probability of false alarm' (SPFA), which is able to do it. We show how this method works in targeted simulations and apply it to a few interferometric maps taken with ALMA and ATCA. We select a few potential new point-sources and assign them an accurate detection reliability.