Volume 16, Issue 1 e1637
Advanced Review

A review of Monte Carlo and quasi-Monte Carlo sampling techniques

Ying-Chao Hung

Corresponding Author

Ying-Chao Hung

Institute of Industrial Engineering, National Taiwan University, Taipei, Taiwan

Correspondence

Ying-Chao Hung, Institute of Industrial Engineering, National Taiwan University, Taipei, Taiwan.

Email: [email protected]

Contribution: Conceptualization (equal), Data curation (equal), Formal analysis (equal), Funding acquisition (equal), ​Investigation (equal), Methodology (equal), Project administration (equal), Resources (equal), Software (equal), Supervision (equal), Validation (equal), Visualization (equal), Writing - original draft (equal), Writing - review & editing (equal)

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First published: 10 November 2023
Edited by: David Scott, Review Editor and Henry Lu, Commissioning Editor

Abstract

This article presents a comprehensive review and comparison of the Monte Carlo and quasi-Monte Carlo sampling techniques, which are widely used in numerical integration, simulation, and optimization. Monte Carlo sampling involves the generation of pseudorandom numbers or vectors to estimate unknown quantities of interest. In contrast, quasi-Monte Carlo sampling is specialized for situations where uniformity and reduced variance are important. It generates a deterministic low-discrepancy sequence that spans the entire sampling space. This review aims to analyze the strengths and distinctions of these two sampling methodologies, offering valuable insights to researchers in search of sampling techniques aligned with their specific research objectives and needs. Furthermore, it seeks to equip practitioners with efficient algorithms for practical implementations.

This article is categorized under:

  • Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods
  • Algorithms and Computational Methods > Numerical Methods
  • Statistical and Graphical Methods of Data Analysis > Sampling

Graphical Abstract

Monte Carlo sampling involves the generation of pseudorandom numbers or vectors to estimate unknown quantities of interest, whilequasi-Monte Carlo sampling generates a deterministic low-discrepancy sequence across the sampling space.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analyzed in this study.