论文标题
删除第一个索博的观点
On dropping the first Sobol' point
论文作者
论文摘要
准蒙特卡洛（QMC）点是普通的蒙特卡洛（MC）点的替代品，在对问题的轻度假设下大大提高了整合精度。因为QMC可以将$ O（1/N）$的错误作为$ n \ to \ infty $，因此甚至更改一个点可以将估计值远大的估计更改，而估计的数量却大得多，并且会使错误率更大。结果，某些与MC点非常自然和直观的实践对QMC的性能非常有害。其中包括稀疏，燃烧和采集样本量，例如$ 10 $的功率，除了设计QMC点的功率。本文着眼于一种共同实践的效果，在这种实践中，人们跳过了Sobol序列的第一点。保留点通常无法成为数字网，当应用争夺时，跳过第一个点可以增加数值误差的因素，与$ \ sqrt {n} $成比例的因素，其中$ n $是所使用的函数评估的数量。
Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are $o(1/n)$ as $n\to\infty$, changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points are very detrimental to QMC performance. These include thinning, burn-in, and taking sample sizes such as powers of $10$, other than the ones for which the QMC points were designed. This article looks at the effects of a common practice in which one skips the first point of a Sobol' sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to $\sqrt{n}$ where $n$ is the number of function evaluations used.
