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