Best-fit model and the likelihood of the parameters from the model of the H₂O lines and the dust continuum in APM 08279+5255. Top left: Observed lensing-corrected (black data points) versus modeled H₂O integrated flux (green and blue are the extended and compact components, respectively; red is the total). Bottom-left: Lensing-corrected modeled dust SED from the two components (same colors as in the top panel). The photometric data are taken from Leung et al. (2019). Right panels: Likelihood distributions of the key parameters of the H₂O model, with the same colors as in the left panels. The arrows indicate the maximum likelihood values (Table 6).