Bayesian analysis of exoplanet and binary orbits Demonstrated using astrometric and radial-velocity data of Mizar A

Aims. We introduce BASE (Bayesian astrometric and spectroscopic exoplanet detection and characterisation tool), a novel program for the combined or separate Bayesian analysis of astrometric and radial-velocity measurements of potential exoplanet hosts and binary stars. The capabilities of BASE are demonstrated using all publicly available data of the binary Mizar A. Methods. With the Bayesian approach to data analysis we can incorporate prior knowledge and draw extensive posterior inferences about model parameters and derived quantities. This was implemented in BASE by Markov chain Monte Carlo (MCMC) sampling, using a combination of the Metropolis-Hastings, hit-and-run, and parallel-tempering algorithms to explore the whole parameter space. Nonconvergence to the posterior was tested by means of the Gelman-Rubin statistic (potential scale reduction). The samples were used directly and transformed into marginal densities by means of kernel density estimation, a smooth alternative to histograms. We derived the relevant observable models from Newton's law of gravitation, showing that the motion of Earth and the target can be neglected. Results. With our methods we can provide more detailed information about the parameters than a frequentist analysis does. Still, a comparison with the Mizar A literature shows that both approaches are compatible within the uncertainties. Conclusions. We show that the Bayesian approach to inference has been implemented successfully in BASE, a flexible tool for analysing astrometric and radial-velocity data.