Monte Carlo Advanced Topics

Monte Carlo - Advanced Topics

The Monte Carlo method
meets Brownian Dynamics
in this simulation of ion
movement in a membrane
channel.

Random Number Generation:

The Monte Carlo method is only as good as the random number generator that it uses. This site has a discussion about RNGs and other criteria used in crafting a Monte Carlo simulation.

All random number generators (RNGs) are not created equal, and the results of a Monte Carlo simulation may depend on the quality of the RNG. Here is a short online book that explains random number generation, and discusses what makes a good or bad generator. The first three chapters are a good introduction, and they only require a working knowledge of algebra.

Most "random number generators" (RNGs) are really pseudo-random number generators (pRNGs). Given enough time, they will repeat the pattern and thus are not truly random. But are they good enough? It depends. For most Monte Carlo simulations with a few thousand samples, a weak pRNG may be sufficient. For those times when a more robust pRNG is required, here is an explanation of what separates the big dogs from the chihuahuas.

A description of tests that can determine the quality of a RNG/pRNG can be found here.

Monte Carlo Simulation:

A full term's worth of lecture notes covering many aspects of Monte Carlo simulation can be found here.

Internet Resources for Monte Carlo Pi: a large compendium of information about computing pi and Buffon's needle.

This resource is an online book that gives a detailed mathematical explanation of the foundations and use of the Monte Carlo method. It requires a very rudimentary knowledge of integral calculus, and knowing some statistics is helpful.