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

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