# Monte Carlo method

The Monte Carlo method is a numerical procedure, devised by S. Ulam (on his hospital bed, playing cards) to solve a problem by randomly sampling it. It is a very powerful method that we use quite a lot. It can apply even to quite unlikely cases (see for instance Knuth's 3:16 study of the Bible).

It is also a favorite for teaching, as it allows one to do nontrivial stuff very quickly. Rejection sampling is both explained and implemented very easily.

A quite advanced but still nice work is by L. Devroye.[1]

## Multivariate sampling

Strangely enough, multivariate sampling—which seems to be a very common need—is little documented on the web, the best thing one can find being people trying to guess the procedure. It is, if taken at face value, a complicated problem, which requires dedicated methods for what are likely highly tricky particular cases that require the method. Even so:

Computational sampling from univariate distributions is effectively a solved problem.
—Dolgov et al.[2]

The simplest method goes as follows: