| Unit name | Monte Carlo Methods |
|---|---|
| Unit code | MATHM6001 |
| Credit points | 10 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Sejdinovic |
| Open unit status | Not open |
| Pre-requisites |
None |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Modern statistics and connected areas very often require the numerical approximation of quantities that are crucial to the understanding of scientific problems as diverse as robot navigation target tracking, wireless communications, epidemiology or genomics to name a few. The Monte Carlo method can be traced back to Babylonian and Old Testament times, but has been systematically used and known under this name since the times of the "Los Alamos School" of physicists and mathematicians in the 1940's-50's. The method is by nature probabilistic and has proved to be a very efficient tool to approximate quantities of interest in various scientific areas. The main idea of Monte Carlo methods consists of reinterpreting mathematical objects, e.g. an integral or a partial differential equation, as the expected behaviour of a quantity related to some random phenomenon. For example p = 3.14 can be thought of as being four times the probability that raindrops falling uniformly on a 2cmx2cm square hit an inscribed disc of radius 1cm. Hence provided that realisations (drops in the example) of the random process (here the &�uniform&� rain) can be observed, it is then possible estimate the quantity of interest by simple averaging. The unit will consist of: (i) showing how numerous important quantities of interest in mathematics and related areas can be related to random processes, and (ii) the description of general probabilistic methods that allow one to simulate realisations of such processes on a standard PC.
