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Module MAP55633: Stochastic Methods

Credit weighting (ECTS)

5 credits

Semester/term taught

First Semester

Module Coordinator

Stefan Sint

Intended Learning Outcomes

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.