Phase diagrams serve as a highly informative tool for materials design,
encapsulating information about the phases that a material can manifest under
specific conditions. In this work, we develop a method in which Bayesian
inference is employed to combine thermodynamic data from molecular dynamics
(MD), melting point simulations, and phonon calculations, process these data,
and yield a temperature-concentration phase diagram. The employed Bayesian
framework yields us not only the free energies of different phases as functions
of temperature and concentration but also the uncertainties of these free
energies originating from statistical errors inherent to finite-length MD
trajectories. Furthermore, it extrapolates the results of the finite-atom
calculations to the infinite-atom limit and facilitates the choice of
temperature, chemical potentials, and the number of atoms conducting the next
simulation with which will be the most efficient in reducing the uncertainty of
the phase diagram. The developed algorithm was successfully tested on two
binary systems, Ge-Si and K-Na, in the full range of concentrations and
temperatures