  Determining the physical characteristics of a star is an inverse problem
consisting in estimating the parameters of models for the stellar structure and
evolution, knowing certain observable quantities. We use a Bayesian approach to
solve this problem for alpha Cen A, which allows us to incorporate prior
information on the parameters to be estimated, in order to better constrain the
problem. Our strategy is based on the use of a Markov Chain Monte Carlo (MCMC)
algorithm to estimate the posterior probability densities of the stellar
parameters: mass, age, initial chemical composition,... We use the stellar
evolutionary code ASTEC to model the star. To constrain this model both seismic
and non-seismic observations were considered. Several different strategies were
tested to fit these values, either using two or five free parameters in ASTEC.
We are thus able to show evidence that MCMC methods become efficient with
respect to more classical grid-based strategies when the number of parameters
increases. The results of our MCMC algorithm allow us to derive estimates for
the stellar parameters and robust uncertainties thanks to the statistical
analysis of the posterior probability densities. We are also able to compute
odds for the presence of a convective core in alpha Cen A. When using
core-sensitive seismic observational constraints, these can raise above ~40%.
The comparison of results to previous studies also indicates that these seismic
constraints are of critical importance for our knowledge of the structure of
this star.
