As we learned in class, the basic principle of the Monte Carlo method is to randomly sample data points and compute their results. These methods are especially useful when we cannot find a definite algorithm for the process, such as finding the volume of an irregular shape.

Thus a foundational tool in any Monte Carlo algorithm is the random number generator that it uses to choose random data points. A common random number generator is the linear congruential generator, which uses the recurrence

the maximum number of random numbers this generator can produce is m, the modulus, and then the sequence will repeat. Thus it is impossible to get truly “random” numbers, instead we can obtain “psuedorandom” numbers, as long as they don’t repeat within the scope of our data.

In this sense, in many Monte Carlo simulations truly random numbers are not needed, but when there is a large number of data points to be sampled, this may cause problems.

For example, physicists at the University of Georgia were using Monte Carlo simulations to show the way some materials suddenly flip into a magnetic state when cooled below a critical temperature.  To their surprise, they found that the computer model consistently predicted the wrong temperature for the transition. Apparently the problem can be attributed to their new random number generator. They were using a new number generator designed by faculty at Florida State University, and although this method produced numbers faster than the linear congruential generator, it proved to be worse in practice. The same numbers can be generated for each method, but for reasons that have yet to be determined the new generator is “less random” than the other.

Thus when using Monte Carlo algorithms, we must be wary of something that may seem trivial, as problems may not be rooted in the algorithm or data but in the creation of random numbers.

http://en.wikipedia.org/wiki/Monte_Carlo_method

http://www.newscientist.com/article/mg13818702.800-science-gambling-on-the-wrong-numbers-from-monte-carlo.html

http://en.wikipedia.org/wiki/Random_number_generator