Uncertainty Quantification and The Need for Better Understanding of Monte Carlo and Random Number Generation

Uncertainty Quantification (UQ) is critical in scientific modeling and decision making, addressing the inherent uncertainty and lack of precision in computational
modeling. Monte Carlo methods, one of the two prominent approaches in UQ, rely on random number generation to simulate complex systems and estimate probability density functions. However, the quality of these methods is naturally tied to the integrity of the random numbers used. Poorly designed random number generators (RNGs) can lead to biased or unreliable results, undermining the validity of UQ. Despite advancements in RNG algorithms, challenges remain in balancing computational efficiency, reproducibility, and randomness quality. A deeper understanding of these generators, their limitations, and their integration with Monte Carlo methods is essential to advancing UQ practices. This technical report tries to highlight keywords in the random number generation field and give a couple of examples showcasing the pitfalls.