Contents of the lecture

Monte Carlo integration

- Monte Carlo integration in 1D: "hit or miss" (or "acceptance-rejection"); "sample mean".

- algorithms to improve the efficiency: importance sampling

- Handling errors: variance reduction with (i) average of the averages (ii) block average  

Multidimensional numerical integration: comparison between deterministic and Monte Carlo methods.

Error analysis

- error in classical methods with equispaced abscissas in one and higher dimensions

- comparison with errors in Monte Carlo method

Metropolis method to generate random number distributions

- Markov chains

- The Metropolis method

- generation of numbers with gaussian distribution using Metropolis method

References:

- Chapter 11 "Numerical Integration" from "Computer simulation Methods" by Gould-Tobochnik (II ed)