The correct estimate of the probability of false detection of the matched filter in weak-signal detection problems

II. Further results with application to a set of ALMA and ATCA data

¹ Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S. Liberale di Marcon, 30020 Venice, Italy
e-mail: robertovio@tin.it
² ESO, Karl Schwarzschild strasse 2, 85748 Garching, Germany
e-mail: pandrean@eso.org
³ École polytechnique, Route de Saclay, 91120 Palaiseau, France

Received: 17 July 2016
Accepted: 6 May 2017

Abstract

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.