  The helioseismic determination of the solar age has been a subject of several
studies because it provides us with an independent estimation of the age of the
solar system. We present the Bayesian estimates of the helioseismic age of the
Sun, which are determined by means of calibrated solar models that employ
different equations of state and nuclear reaction rates. We use 17 frequency
separation ratios
$r_{02}(n)=(\nu_{n,l=0}-\nu_{n-1,l=2})/(\nu_{n,l=1}-\nu_{n-1,l=1})$ from 8640
days of low-$\ell$ BiSON frequencies and consider three likelihood functions
that depend on the handling of the errors of these $r_{02}(n)$ ratios.
Moreover, we employ the 2010 CODATA recommended values for Newton's constant,
solar mass, and radius to calibrate a large grid of solar models spanning a
conceivable range of solar ages. It is shown that the most constrained
posterior distribution of the solar age for models employing Irwin EOS with
NACRE reaction rates leads to $t_\odot = 4.587 \pm 0.007$ Gyr, while models
employing the Irwin EOS and Adelberger, et al., Reviews of Modern Physics, 83,
195 (2011) reaction rate have $t_\odot = 4.569 \pm 0.006 $ Gyr. Implementing
OPAL EOS in the solar models results in reduced evidence ratios (Bayes factors)
and leads to an age that is not consistent with the meteoritic dating of the
solar system. An estimate of the solar age that relies on an helioseismic age
indicator such as $r_{02}(n)$ turns out to be essentially independent of the
type of likelihood function. However, with respect to model selection,
abandoning any information concerning the errors of the $r_{02}(n)$ ratios
leads to inconclusive results, and this stresses the importance of evaluating
the trustworthiness of error estimates.
