Hi I just wondered if the probability densities have to be corrected when using them on a PC since the number representation is not at all continuous. So we cant simulate any irrational numbers and are missing a lot of number which decimals we cant represent due to limitations of the data type double for example. Does one account for such problems when doing Monte Carlo simulations for example? Or is the amount of error just to little to care about? And if so - how does one compute such an error?
2025-01-13 02:37:18.1736735838
Mistake in generating random numbers - no irrational ones
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In over 20 years of applied work, this has never been a problem. As you put it, the amount of error is too small to be of concern. I can't imagine ever needing more than 6 decimals of accuracy in a summary statistic, and for most work 2 decimals are sufficient. The modeling error and noise in real-world problems far exceeds any issues in using rational variates in a simulation.