Assessing the Impact of Computational Precision on Statistical Simulation Accuracy and Reproducibility

Posted: Jun 17, 2025

• David Gray
• Eleanor Butler
• Elena Scott

Abstract

Computational statistics has revolutionized empirical research across scientific disciplines, enabling complex simulations that would be analytically intractable. However, the fundamental relationship between computational precision and simulation outcomes remains inadequately understood. While numerical analysis has long recognized the importance of precision in mathematical computations, the specific implications for statistical simulation—where randomness, convergence, and reproducibility interact with numerical precision—have received surprisingly little systematic investigation. This research addresses this critical gap by examining how computational precision influences both the accuracy and reproducibility of statistical simulations. The prevailing assumption in statistical computing has been that higher precision universally improves simulation quality, leading to a default preference for double-precision arithmetic in most statistical software. However, this assumption overlooks the complex interplay between precision, algorithmic stability, and statistical properties. Our research challenges this conventional wisdom by demonstrating that the relationship between precision and simulation quality is nuanced and context-dependent. We investigate whether there exist optimal precision levels for different types of statistical simulations and whether precision requirements can be predicted from simulation characteristics. This study makes several original contributions to computational statistics. First, we develop a novel methodological framework for precision-aware statistical simulation that enables systematic manipulation of computational precision while controlling for other factors. Second, we identify precision thresholds for common statistical procedures that balance computational efficiency with simulation quality. Third, we demonstrate that precision-induced errors follow distinctive patterns across different simulation types, revealing underlying mathematical structures that were previously unrecognized.