The video states that the earlier example 'cheated' because the rare event was not very rare, making direct rejection sampling from computationally feasible. In general, for truly rare events, direct rejection sampling would take too long, which motivates the use of the adaptive cross-entropy method.
Conditions: The context is comparing the improved cross-entropy method to the original cross-entropy method.; The rare event in the earlier example had a relatively high probability.
The video states that the earlier example 'cheated' because the rare event was not very rare, making direct rejection sampling from computationally feasible. In general, for truly rare events, direct rejection sampling would take too long, which motivates the use of the adaptive cross-entropy method.
Conditions: The context is comparing the improved cross-entropy method to the original cross-entropy method.; The rare event in the earlier example had a relatively high probability.