Monte Carlo Method

Approximation by repeated random sampling (probabilistic simulation)

Integration technique usually to transform discrete to continuous distribution. For example when we compute the expectation of where has density

Assume we have a way of drawing samples from density , we can approximate the integral above by (with access of function and

This is unbiased estimator: It approximates better as grows.

Assume you have a difficult integral to compute

In short, Monte Carlo methods enable us to estimate any integral by random sampling. In

Evidence is also form of integral so it becomes tractable.

Since it is

In other words, as , the variance goes to zero.

Monte Carlo Methods