We consider the space-debris orbital inversion problem via the concept of Bayesian inference. The methodology has been put forward for the orbital analysis of solar system small bodies in early 1990's  and results in a full solution of the statistical inverse problem given in terms of a posteriori probability density function (PDF) for the orbital parameters. We demonstrate the applicability of our statistical orbital analysis software to Earth orbiting objects, both using well-established Monte Carlo (MC) techniques (for a review, see e.g.  as well as recently developed Markov-chain MC (MCMC) techniques (e.g., ). In particular, we exploit the novel virtual observation MCMC method , which is based on the characterization of the phase-space volume of orbital solutions before the actual MCMC sampling. Our statistical methods and the resulting PDFs immediately enable probabilistic impact predictions to be carried out. Furthermore, this can be readily done also for very sparse data sets and data sets of poor quality - providing that some a priori information on the observational uncertainty is available. For asteroids, impact probabilities with the Earth from the discovery night onwards have been provided, e.g., by  and , the latter study includes the sampling of the observational-error standard deviation as a random variable.