Note: On the Value of Function Evaluation Location Information in Monte Carlo Simulation
针对一维积分问题，证明若根据函数评估位置调整权重，可将蒙特卡洛估计的收敛速度从n的负二分之一次方提升至n的负二次方，对改进模拟效率有参考价值。
The point estimator used in naive Monte Carlo sampling weights all the computed function evaluations equally, and it does not take into account the precise locations at which the function evaluations are made. In this note, we consider one-dimensional integration problems in which the integrand is twice continuously differentiable. It is shown that if the weights are suitably modified to reflect the location information present in the sample, then the convergence rate of the Monte Carlo estimator can be dramatically improved from order n −1/2 to order n −2 , where n is the number of function evaluations computed.