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tokens: is not taken into account. The observed seismic diagnostics are indicated in Fig. 1 . I also show the best model for each case in Tables 3 and 4 (red thin lines). These optimal theoretical values are barely distinguishable from one model to the other. This indicates that they may be equally valid in order to reproduce the data, and that statistical model comparison methods (see e.g. Robert 2007 , Chap. 7) alone will not suffice to distinguish them. Further discussions on model comparison are given in Sects. 3.2 and 3.1 . Visual inspection of Fig. 1 also indicates that the accuracy of the present results is similar to what was obtained by Metcalfe et al. (2015) . Figure 2 shows the MAP estimates of all non-seismic observations. They are all reproduced with good accuracy, within 1 σ of the observed values. Fig. 1. Seismic diagnostic for 16 Cyg A ( left panel ) and B ( right panel ). The squares, triangles, and circles denote the observed r 13 , r 02 , and r 01 observed ratios, respectively. The red lines show the best models for all runs in Tables 3 and 4 . Fig. 2. Non-seismic observations for 16 Cyg A ( left panel ) and B ( right panel ). The horizontal lines represent the observed values (full lines) and the corresponding uncertainties (dashed lines). The dots denote the estimated values (MAPs of the marginal densities) for the corresponding observation, for each run. The runs are labelled on the abscissa according to the numbering given in Tables 3 and 4 . The two-dimensional joint PDFs for this set-up are shown in Fig. 3 alongside the corresponding correlation coefficients. The mass correlates most significantly with X 0 . The age correlates extremely well with the mixing-length parameter and slightly less with X 0 . It may be counter-intuitive that the mass does not correlate strongly with the age. A likely explanation is that, due to the level of constraint imposed by the seismic data, these two parameters cannot vary enough to allow such a correlation to be observed. Interpreting these correlations is not straightforward because there is in general no one-to-one correspondence between a parameter and an observation. Thus elements of interpretation can be gathered by looking at the correlation between the stellar parameters and other quantities. The mass and X 0 (Pearson correlation coefficients ≳0.8) both correlate strongly with the luminosity and the radius on the zero-age main sequence (ZAMS). This is related to the mass-luminosity relation on the ZAMS, in which the mean-molecular weight enters (see e.g. Clayton 1968 ). To maintain a roughly constant luminosity, an increase in mass must be compensated by a decrease in the mean-molecular weight. This latter corresponds to an increase in the initial hydrogen-mass fraction and a decrease of the initial helium-mass fraction because the two quantities are perfectly anti-correlated. The interaction between the mass and the hydrogen-mass fraction thus sets the initial conditions of the