Editing Monte Carlo method (section)

===Monte Carlo and random numbers===

The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known.
Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally.<ref name="usaus">{{cite journal|author-last1=Shojaeefard |author-first1=M.H. |author-last2=Khalkhali |author-first2=A. |author-last3=Yarmohammadisatri |first3=Sadegh |title=An efficient sensitivity analysis method for modified geometry of Macpherson suspension based on Pearson Correlation Coefficient |journal=Vehicle System Dynamics |volume=55 |issue=6 |pages=827–852 |doi=10.1080/00423114.2017.1283046 |year=2017 |bibcode = 2017VSD....55..827S |s2cid=114260173}}</ref> Monte Carlo simulation methods do not always require [[Random number generation#True vs. pseudo-random numbers|truly random number]]s to be useful (although, for some applications such as [[primality testing]], unpredictability is vital).<ref>{{harvnb|Davenport|1992}}</ref> Many of the most useful techniques use deterministic, [[pseudorandom number generator|pseudorandom]] sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good [[simulation]]s is for the pseudo-random sequence to appear "random enough" in a certain sense.

What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are [[Uniform distribution (continuous)|uniformly distributed]] or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.

Sawilowsky lists the characteristics of a high-quality Monte Carlo simulation:<ref name=Sawilowsky/>
* the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats)
* the (pseudo-random) number generator produces values that pass tests for randomness
* there are enough samples to ensure accurate results
* the proper sampling technique is used
* the algorithm used is valid for what is being modeled
* it simulates the phenomenon in question.

[[Pseudo-random number sampling]] algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given [[probability distribution]].

[[Low-discrepancy sequences]] are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences. Methods based on their use are called [[quasi-Monte Carlo method]]s.

In an effort to assess the impact of random number quality on Monte Carlo simulation outcomes, astrophysical researchers tested cryptographically secure pseudorandom numbers generated via Intel's [[RDRAND]] instruction set, as compared to those derived from algorithms, like the [[Mersenne Twister]], in Monte Carlo simulations of radio flares from [[brown dwarfs]]. No statistically significant difference was found between models generated with typical pseudorandom number generators and RDRAND for trials consisting of the generation of 10<sup>7</sup> random numbers.<ref>{{cite journal|author-last1=Route |author-first1=Matthew |title=Radio-flaring Ultracool Dwarf Population Synthesis |journal=The Astrophysical Journal |date=August 10, 2017 |volume=845 |issue=1 |page=66 |doi=10.3847/1538-4357/aa7ede |arxiv=1707.02212 |bibcode=2017ApJ...845...66R |s2cid=118895524 |doi-access=free }}</ref>