Monte Carlo Integration: Review
Stochastic evaluation of integrals
- sum integrand evaluated at randomly generated points
- most appropriate for high-dimensional integrals
error vanishes more quickly (1/n1/2)
better suited for complex-shaped domains of integration
Monte Carlo simulation
- Monte Carlo integration for ensemble averages
Importance Sampling
- emphasizes sampling in domain where integrand is largest
- it is easy to generate points according to a simple distribution
- stat mech p distributions are too complex for direct sampling
- need an approach to generate random multidimensional points according to a complex probability distribution
- then integral is given by