  This work introduces two Monte Carlo (MC)-based sampling methods, known as
line sampling and subset simulation, to improve the performance of standard MC
analyses in the context of asteroid impact risk assessment. Both techniques
sample the initial uncertainty region in different ways, with the result of
either providing a more accurate estimate of the impact probability or reducing
the number of required samples during the simulation with respect to standard
MC techniques. The two methods are first described and then applied to some
test cases, providing evidence of the increased accuracy or the reduced
computational burden with respect to a standard MC simulation. Finally, a
sensitivity analysis is carried out to show how parameter setting affects the
accuracy of the results and the numerical efficiency of the two methods.
