Monte Carlo Methods

1. Introduction 


2. Basics of direct Monte Carlo - will introduce the basic idea of direct Monte Carlo and how one estimates the error involved. 

3. Pseudo-Random Number Generators - general structure of such generators and how one tests them 

4. Generating non-uniform random variables - how you can use random numbers that are uniformly distributed on [0, 1] to generate samples of a random variable with either a continuous or discrete distribution. 

5. Variance Reduction

6. Importance Sampling 

7. Markov chain background 

8. Markov chain Monte Carlo 

9. Convergence and error bars for MCMC 

10. Optimization 

11. Further Topics