Statistical analysis of probability density functions for photometric redshifts through the KiDS-ESO-DR3 galaxies

Despite the high accuracy of photometric redshifts (zphot) derived using machine learning (ML) methods, the quantification of errors through reliable and accurate probability density functions (PDFs) is still an open problem. First, because it is difficult to accurately assess the contribution from different sources of errors, namely internal to the method itself and from the photometric features defining the available parameter space. Secondly, because the problem of defining a robust statistical method, always able to quantify and qualify the PDF estimation validity, is still an open issue. We present a comparison among PDFs obtained using three different methods on the same data set: two ML techniques, METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) and ANNz2 , plus the spectral energy distribution template-fitting method, BPZ (Bayesian photometric redshift). The photometric data were extracted from the Kilo Degree Survey ESO Data Release 3, while the spectroscopy was obtained from the Galaxy and Mass Assembly Data Release 2. The statistical evaluation of both individual and stacked PDFs was done through quantitative and qualitative estimators, including a dummy PDF, useful to verify whether different statistical estimators can correctly assess PDF quality. We conclude that, in order to quantify the reliability and accuracy of any zphot PDF method, a combined set of statistical estimators is required.