Summary
Monte Carlo methods use stochastic process to answer a non-stochastic question
- generate a random sample from an ensemble
- compute properties as ensemble average
- permits more flexibility to design sampling algorithm
Monte Carlo integration
- good for high-dimensional integrals
better error properties
better suited for integrating in complex shape
Importance Sampling
- focuses selection of points to region contributing most to integral
- selecting of weighting function is important
- choosing perfect weight function is same as solving integral
Next up:
- Markov processes: generating points in a complex region