0
monte carlo simulation methods do not always require truly random numbers to be useful — while for some applications, such as primality testing, unpredictability is vital.[10] many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. the only quality usually necessary to make good simulations 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 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.
sawilowsky lists the characteristics of a high quality monte carlo simulation:[9]
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 methods.
