Context :

Aims : We aim to perform a theoretical investigation on the direct impact of measurement errors in the observational constraints on the recovered age for stars in main sequence ( MS ) and red giant branch ( RGB ) phases .
We assumed that a mix of classical ( effective temperature T _ { eff } and metallicity [ Fe/H ] ) and asteroseismic ( \Delta \nu and \nu _ { max } ) constraints were available for the objects .

Methods : Artificial stars were sampled from a reference isochrone and subjected to random Gaussian perturbation in their observational constraints to simulate observational errors .
The ages of these synthetic objects were then recovered by means of a Monte Carlo Markov chains approach over a grid of pre-computed stellar models .
To account for observational uncertainties the grid covers different values of initial helium abundance and mixing-length parameter , that act as nuisance parameters in the age estimation .

Results : The obtained differences between the recovered and true ages were modelled against the errors in the observables .
This procedure was performed by means of linear models and projection pursuit regression models .
The first class of statistical models provides an easily generalizable result , whose robustness is checked with the second method .
From linear models we find that no age error source dominates in all the evolutionary phases .
Assuming typical observational uncertainties , for MS the most important error source in the reconstructed age is the effective temperature of the star .
An offset of 75 K accounts for an underestimation of the stellar age from 0.4 to 0.6 Gyr for initial and terminal MS. An error of 2.5 % in \nu _ { max } resulted the second most important source of uncertainty accounting for about -0.3 Gyr .
The 0.1 dex error in [ Fe/H ] resulted particularly important only at the end of the MS , producing an age error of -0.4 Gyr .
For the RGB phase the dominant source of uncertainty is \nu _ { max } , causing an underestimation of about 0.6 Gyr ; the offset in the effective temperature and \Delta \nu caused respectively an underestimation and overestimation of 0.3 Gyr .
We find that the inference from the linear model is a good proxy for that from projection pursuit regression models .
Therefore , inference from linear models can be safely used thanks to its broader generalizability .
Finally , we explored the impact on age estimates of adding the luminosity to the previously discussed observational constraints .
To this purpose , we assumed – for computational reasons – a 2.5 % error in luminosity , much lower than the average error in the Gaia DR2 catalogue .
However , even in this optimistic case , the addition of the luminosity does not increase precision of age estimates .
Moreover , the luminosity resulted as a major contributor to the variability in the estimated ages , accounting for an error of about -0.3 Gyr in the explored evolutionary phases .

Conclusions :