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tokens: the 2MASS All Sky Data Release. 4 The zero-points with their standard errors are taken from Maíz Apellániz Pantaleoni González ( 2018 ). For the WISE photometry, we calculate synthetic magnitudes on the AB magnitude scale and then apply the corrections to Vega magnitudes from Jarrett et al. ( 2011 ) for which the estimated error is 1.45 per cent (0.016 mag). For the IUE NEWSIPS spectra, we adopted a zero-point error of 4 per cent from Nichols Linsky ( 1996 ). 3.3 Interstellar reddening Fig. 3 shows a selection of HARPS spectra of AI Phe obtained from the ESO Science Archive Facility in the region of the Na i doublet. There are no detectable interstellar absorption lines in this region and so the reddening towards AI Phe must be very close E ( B − V ) = 0 (Karataş Schuster 2010 ). Accordingly, we set a Gaussian prior on the reddening E ( B − V ) = 0 ± 0.005 and set a lower limit E ( B − V ) ≥ 0. Figure 3. HARPS spectra of AI Phe in the region of the Na i doublet. The spectra have been normalized and vertically offset for clarity. The rest wavelengths of the Na i lines are indicated by vertical dashed lines. 3.4 Priors on infrared flux ratios The near-infrared (NIR) flux from solar-type stars compared to the total flux or the flux at optical wavelengths shows a well-defined relationship with T eff that is almost linear and that has little dependence on metallicity or surface gravity. This is the basis of the infrared flux method (Blackwell, Shallis Selby 1979 ; Casagrande et al. 2010 ) or the use of colours such as () to estimate effective temperatures for FGK-type stars (Boyajian et al. 2013 ). There is only one direct measurements of the flux ratio for AI Phe at wavelengths longer than 1 μm. We were concerned that not imposing any additional constraints on the flux ratio at these wavelengths could mean that the resulting models become unrealistic, e.g. the () colours computed using samples from P ( M | D ) might show a much large scatter than is observed in real stars. This could happen if the use of distortion coefficients allows for models where the flux from one star is unrealistically high at NIR wavelengths while the other is too low, unless some constraint is placed on the flux ratio at these wavelengths. We address this concern by making the assumption that the stars in AI Phe behave similarly to other dwarf and sub-giant FGK-type stars in the solar neighbourhood in order to put some constraint on the flux ratio in the 2MASS J, H , and K s bands, and the WISE W 1, W 2, W 3, and W 4 bands. We use stars from the Geneva–Copenhagen survey (Holmberg et al. 2009 ) to define relationships between T eff and ( V − J ), ( V − H ), etc. The values of T eff , E ( B − V ), log g , and [Fe/H] for each star are taken from Casagrande et al. ( 2011 ). We define separate relations for the F7 V star and the K0 IV star based on a different subsample of stars with similar properties to each. For the F7 V star, the subsample is defined by the following