The video states that the earlier example 'cheated' because the rare event was not very rare, making direct rejection sampling from g∗ 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 g∗ 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 confidence interval is constructed as a symmetric interval around the point estimate. The half-width is calculated by multiplying 1.96 by the sample standard deviation of the weighted estimator array, and then dividing by the square root of the number of proposal samples.
Conditions: Uses the sample standard deviation of the weighted estimates.; The interval is presented as a numerical summary based on a normal approximation.
The confidence interval is constructed as a symmetric interval around the point estimate. The half-width is calculated by multiplying 1.96 by the sample standard deviation of the weighted estimator array, and then dividing by the square root of the number of proposal samples.
Conditions: Uses the sample standard deviation of the weighted estimates.; The interval is presented as a numerical summary based on a normal approximation.