 
Summary: A survey of Monte Carlo methods
Jonathan Weare
University of Chicago
April 5, 2011
Jonathan Weare A survey of Monte Carlo methods
Basic goal
Calculate averages,
E [g(X)] = g(x)p(dx),
over a probability distribution (or density), p (X is a sample from
p), describing the states of complex systems.
In more than a few dimensions we can't use quadrature
methods. They require Nd grid points for a fixed accuracy.
A Monte Carlo scheme requires (in principle) N2 samples to
achieve a fixed accuracy. But the prefactor can be huge.
When deterministic methods are applicable they are usually
better... but many (most?) problems are high dimensional so
we need MC.
Jonathan Weare A survey of Monte Carlo methods
Some high dimensional applications
Equilibrium sampling in a Chemical system, e.g. what
