Students who successfully complete the course should be able to:

Employ a range of techniques for generating random numbers according to different distributions.

Describe and employ basic concepts in probability and statistical inference.

Implement the jack knife and bootstrap resampling methods to estimate statistical errors.

Apply variance reduction techniques to stochastic estimates of integration problems.

Describe and use basic concepts in the theory of Markov processes as well as common simulation algorithms.

Implement common Markov chain Monte Carlo algorithms to simulate benchmark statistical systems.

Structure and Content

The module covers an introduction to stochastic and statistical methods in computer simulation. After a brief revision of statistics and probability, the course will cover;

Pseudo-random number generation, including generation according to arbitrary distributions.

Basic ideas of Monte Carlo integration, including variance reduction techniques such as stratified sampling, antithetic variables, and importance sampling.

Statistical inference and the statistical analysis of data, in particular the non-parametric jack knife and bootstrap estimation techniques.

An introduction to Markov Chain Monte Carlo, and its application to problems in physics, mathematics, and chemistry.

Assessment Detail

40% continuously assessed assignments. 60% written examination.