Module Descriptor 2012/13
School of Computer Science and Statistics.
Module Code
Module Name
Module Short
Title
ST2004
Modelling Uncertainty and Random Variation with Monte Carlo Methods
Modelling Uncertainty
ECTS
weighting
5
Semester/term
taught
Michaelmas
Contact Hours
Lecture hours:
Lab hours:
Tutorial hours:
24
6
6
Total hours:
36
Module
Personnel
Learning
Outcomes
Module
Learning Aims
Lecturing staff: Prof J Haslett and demonstrators
Students will have ability

to build a model in a spreadsheet or similar using random numbers

to analyse via summaries of many replications

in some circumstances to bypass these steps by using probability

to use the formal language of random variables, their expected values, and
their probability distributions

to use conditional distributions
Uncertainty and/or variation that is random or unpredictable is a central challenge
in devising efficient systems. Examples include a Google search, student
progression given imprecise marking, a pension scheme, the evaluation of financial
derivatives, and more generally planning in an uncertain environment given
imprecise or inadequate data. This course aspires to build confidence in the
manipulation of uncertain information. Additionally randomness is deliberately
introduced in security systems, and exploited in computer graphics. The central tool
is the use probability to model or approximate a system.
In this course we take a novel approach that replaces mathematics with the use of
‘random numbers’ in a spread sheet – or more generally an algorithm; this is known
as the Monte Carlo method (http://en.wikipedia.org/wiki/Monte_Carlo_method).
Students will rapidly acquire the facility to model quite complex random (or
stochastic) systems. They will subsequently learn the language of probability which
can sometimes by-pass the algorithms, or render them more efficient.
Module
Content
Specific topics addressed in this module include:
 RAND() and Uniform Random Numbers (Monte Carlo) in EXCEL
o Random games and random passwords
Page 1 of 2
Module Descriptor 2012/13
School of Computer Science and Statistics.
o Random Systems
o Transformations of random numbers
o Conditional and rejection algorithms
• Properties and summaries of random systems
o The long run properties of random numbers (law of large numbers)
o Univariate random variables and the cumulative probability distribution
function
o Properties of Monte Carlo algorithms
•
o
o
o
o
The concepts underlying probability, including
The basic rules
Discrete and continuous univariate random variables
cumulative distribution functions
Probability mass functions, density functions and Expected values, variances
and standard deviations
o Frequently used univariate probability distributions
o Bivariate and multivariate probability distributions
o Covariance and correlation
Recommended
Reading List
Wikipedia: http://en.wikipedia.org/wiki/Monte_Carlo_method
Main text Tijms, “Understanding Probability”, Cambridge 2007.
A second edition was published July 2012
Module Pre
Requisite
Elementary mathematics including summation and integration.
Module Co
Requisite
For MSISS, ST2005
Assessment
Details
Exam, two compulsory group projects (5% and 10%) and one optional project (30%)
Description of assessment & assessment regulations.
Module
approval date
N/a
Approved By
N/a
Academic
Start Year
2012-2013
Academic Year
2012
of Data
Page 2 of 2