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Module MA5634: Stochastic Methods

Credit weighting (ECTS)
5 credits
Semester/term taught
First Semester 2016-17
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.