Covariance estimation using h-statistics in Monte Carlo and multilevel Monte Carlo methods

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-01 DOI:10.1615/int.j.uncertaintyquantification.2024051528

Sharana Kumar Shivanand

引用次数: 0

Abstract

We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's mean square error in a closed form. This is in contrast to conventional MC and MLMC covariance estimators, which are based on biased mean square errors defined solely by upper bounds, particularly within the MLMC. The numerical results of the algorithms are demonstrated by estimating the covariance of the stochastic response of a simple 1D stochastic elliptic PDE such as Poisson's model.

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在蒙特卡洛和多级蒙特卡洛方法中使用 h 统计量进行协方差估计

我们提出了新颖的蒙特卡罗（MC）和多级蒙特卡罗（MLMC）方法，利用 h 统计法确定随机变量的无偏协方差。这种方法的优势在于能以封闭形式无偏构建估计器的均方误差。这与传统的 MC 和 MLMC 协方差估计器形成了鲜明对比，后者基于仅由上界定义的有偏均方误差，尤其是在 MLMC 内。通过估计泊松模型等简单一维随机椭圆 PDE 的随机响应协方差，演示了算法的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.