Magíster en Ciencias de la Ingeniería, Mención Eléctrica / Mass is arguably the most important property of a star: along with the initial distribution of chemical elements, stellar mass is responsible for the evolution and structure of these objects. The only means for calculating the mass of a star is the study of its orbital movement, for Kepler s Third Law establishes a strict mathematical relation between mass and orbital parameters. Since single stars do not follow orbital trajectories, the observational base of the stellar mass catalog consists mainly of binary and multiple stars; hence the importance of studying their orbits. This dissertation addresses the problem of characterizing the orbits of binary stars from a Bayesian standpoint, approximating the posterior probability density functions of orbital elements by means of the technique known as Markov Chain Monte Carlo. A selection of 18 visual and 2 spectroscopic binary stars observed by the SOAR telescope are analyzed with the proposed technique, obtaining not only orbit estimates of each object (maximum a posteriori for visual binaries, expected value for spectroscopic binaries), but also a characterization of their uncertainty in the form of posterior distributions of orbital elements. By using a mathematical formalism developed as a part of this work, the dimension of the target parameter vector is reduced from 7 to 3 in the case of visual binaries, and from 10 to 7 for spectroscopic binaries. The potential of combining astrometric and spectroscopic sources for estimating hypothesis-free parameters is explored, concluding that good estimations can be obtained if both the apparent orbit and the radial velocity profile of the star can be independently characterized. This work also introduces a strategy to incorporate partial astrometric observations (measurements where either angular separation or position angle is missing) into the proposed Bayesian framework. This strategy combines the MCMC-based estimation of orbital parameters with the multiple imputation approach: instead of being discarded as an input for the parameter estimation routines, incomplete observations are replaced by a set of plausible values, incorporating this partial knowledge into the analysis. This methodology is tested on both synthetic and real data, obtaining not only the distribution of parameters given all observations available (complete and partial ones), but also an estimation of the spatial localization of partial measurements. Results suggest that the incorporation of partial knowledge can lead to a decrease in the uncertainty associated to target parameters (dramatic in some cases); however, partial information can also be redundant in some scenarios.