Log likelihood of quasars (left), dwarf stars (middle), and low-redshift galaxies (right) modelled by a Gaussian mixture model in colour space. The red ellipses indicate the 3-sigma extents of the individual deconvolved Gaussians (four components for quasars, six for dwarf stars, and one for galaxies). The quasar likelihoods are assigned using photometry from simulated quasar spectra as highlighted in Sect. 3.1, whereas the photometry for dwarf stars and low-redshift galaxies are taken from their respective reference catalogues, Best et al. (2017) and Williams et al. (2018) (black dots). The dashed line in the left panel marks the commonly defined colour cut at i − z = 2.0.