A method for the identification of orbital conjunctions and the computation of the collision probability between two space objects is presented. The method is based on the Taylor expansion of both the time and the distance of closest approach between the two orbiting objects with respect to their uncertain initial positions and velocities. The collision probability is then computed via Monte Carlo simulations, taking advantage of the availability of analytical information to speed up the analysis. The efficiency of the proposed approach is further improved by adopting two advanced Monte Carlo techniques: Line Sampling and Subset Simulation. The resulting method applies on a wide range of orbits since no simplifications on the conjunction event are assumed. Test cases are run on LEO and GEO encounters. The standard and advancedMonte Carlo methods are compared in terms of collision probabilities and computational efficiency.