We evaluate asteroid orbital uncertainties from the discovery night onwards using 6D orbit computation tools based on statistical techniques. In particular, we outline a new nonlinear Monte Carlo technique of phase-space sampling that helps us in assessing the nonlinear phase transition from extended orbital-element distributions to well-constrained ones as the observational arc and number of observations grows. We apply the statistical techniques for near-Earth asteroid 2004 AS$_1$ to examine the time evolution of the orbital uncertainties and to assess the asteroid impact risk immediately after discovery. We start with the technique of statistical ranging for exiguous data, continue with the phase-space sampling technique for moderate data, and conclude with the standard least-squares fit for extensive data.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html