Guaranteed Conservative Fixed Width Confidence Intervals Via Monte Carlo Sampling
Guaranteed Conservative Fixed Width Confidence Intervals Via Monte Carlo Sampling
复制标题
通过蒙特卡罗采样保证保守的固定宽度置信区间
DOI：
10.1007/978-3-642-41095-6_5
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Owen
中科院分区：
文献类型：
--
作者：
F. J. Hickernell;Lan Jiang;Yuewei Liu;A. Owen
蒙特卡洛方法用于近似随机变量y的均值，其分布不知道，关键的想法是随机样本的平均值，y 1，…，y n倾向于μ无穷大。用户指定的界限。 µ讨论\（\ boldsymbol {x}）\）和\（\ boldsymbol {x} \）的重要情况。解释为积分\（\ int _ {{\ Mathbb {r}}}^{d}}} f（\ boldsymbol {x}）\ rho（\ boldsymbol {x}） {x} \），蒙特卡洛方法成为多维立方体的方法。
Monte Carlo methods are used to approximate the means, μ, of random variables Y, whose distributions are not known explicitly. The key idea is that the average of a random sample, Y 1, …, Y n , tends to μ as n tends to infinity. This article explores how one can reliably construct a confidence interval for μ with a prescribed half-width (or error tolerance) \(\varepsilon\). Our proposed two-stage algorithm assumes that the kurtosis of Y does not exceed some user-specified bound. An initial independent and identically distributed (IID) sample is used to confidently estimate the variance of Y. A Berry-Esseen inequality then makes it possible to determine the size of the IID sample required to construct the desired confidence interval for μ. We discuss the important case where \(Y = f(\boldsymbol{X})\) and \(\boldsymbol{X}\) is a random d-vector with probability density function ρ. In this case μ can be interpreted as the integral \(\int _{{\mathbb{R}}^{d}}f(\boldsymbol{x})\rho (\boldsymbol{x})\,\,\mathrm{d}\boldsymbol{x}\), and the Monte Carlo method becomes a method for multidimensional cubature.