Core A (Calculus/Probability)
The applications of probability are diverse, occurring in industry,
mathematics, science, technology, medicine, social science, agriculture,
etc. In this course the theory of probability is developed but always
with applications in mind. Among the topics covered are: probability
axioms, conditional probability, special distributions, random variables,
expectations, generating functions, applications of probability,
laws of large numbers, central limit theorems.
Statistical Concepts II
Anyone who collects information must decide how to draw useful
conclusions from it. For example, can an opinion poll involving
maybe 1000 people, be trusted to give an accurate picture of everyone
else's opinions? Answering this question requires that we combine
our knowledge of probability theory with our understanding of how
opinion polls are performed. The kind of reasoning that results
is called statistical inference.
Other areas of popular debate where statistical problems arise
include understanding the effects of food additives, interpreting
the results of clinical trials of medical treatments, the reliability
of electrical and other products and the incidence of leukemia near
nuclear power stations. A knowledge of statistics is essential not
only to those who specialise in studying such phenomena but also
to anyone who wishes to develop informed opinions about them. The
module will introduce some basic ideas of statistical inference
and develop solutions to some standard problems. There are two schools
of thought about the fundamental principles of statistics, the Bayesians
and the frequentists. The module covers both viewpoints but the
majority of methods presented will be the more widely used frequentist
Practical computing sessions, using the freely available statistical
package R, will be held throughout the year. They serve two purposes:
to bring the module closer to the real world of applied statistics
and provide additional insight into the lectured material.
Decision Theory III
Decision theory concerns problems where we have a choice of decision,
and the outcome of our decision is uncertain (which describes most
problems!). The main topic of the course is statistical decision
theory from a Bayesian point of view, and it further includes several
introductory presentations of interesting fields of practical decision
The course starts with an introduction to the ideas of decision
analysis and the use of decision trees. Quantification of rewards
(by means of utilities) and uncertainties (by means of subjective
probabilities) are discussed, and these together form the basis
of Bayesian statistical decision theory. Formal methods to use data
in decision making are presented, including some attention to sequential
analysis. Finally, some attention is paid to group decision making,
bargaining and game theory.
Operations Research III
As its name implies, operations research involves "research
on operations", and it is applied to problems that concern
how to conduct and coordinate the operations (activities) within
an organisation. The nature of the organisation is essentially immaterial,
and, in fact, OR has been applied extensively in such diverse areas
as manufacturing, transportation, construction, telecommunications,
financial planning, health care, the military and public services
to name just a few.
This course is an introduction to mathematical models in operations
research. Usually, a mathematical model of a practical situation
of interest is developed, and analysis of the model is aimed at
gaining more insight into the real world. Many problems that occur
ask for optimisation of a function f under some constraints.
This method is introduced and applied to several problems, e.g.
Many situations of interest in OR involve processes with random
aspects and we will introduce stochastic processes to model such
situations. An interesting area of application, addressed in this
course, is inventory theory, where both deterministic and stochastic
models will be studied and applied. Further topics will be chosen
from: Markov decision processes; integer programming; nonlinear
programming; dynamic programming.
Statistical Methods III
The course introduces widely used statistical methods, with theoretical
issues kept to a minimum. The course, which includes statistical
computing, regression, generalised linear models and multivariate
analysis, should be of particular interest to those who intend to
follow a career in statistics.
Stochastic Processes III (B)
A stochastic process is a mathematical model for a system evolving
randomly in time. For example, the size of a biological population
or the price of a share may vary in an unpredictable manner. These
and many other systems in the physical sciences, biology, economics,
engineering and computer sciences may best be modeled in a non-deterministic
manner. More technically, a stochastic process is a collection of
random quantities indexed by a time parameter. Typically, these
quantities are not independent, but have their dependency structure
specified via the time parameter. Specific models to be covered
include Markov chains in discrete and continuous time, Poisson processes
and Gaussian processes.
Bayesian Statistics IV
This course provides an overview and substantial practical applications
in Bayesian statistics. The course starts with an introduction to
'the Bayesian approach', which includes discussion of foundational
issues. This is followed by Bayesian forecasting, including discussion
of the forecast cycle and working towards good understanding of
dynamic linear models, also considering important related aspects
such as diagnostics and remodelling.
Another main topic is Bayesian computation, in particular Markov
Chain Monte Carlo techniques with applications to Bayesian graphical
models, exploring conditional independence assumptions. Examples
may include spatial smoothing, image processing and medical diagnosis.
The course ends with attention to Bayes linear methods. This combines
interesting foundational aspects with clear presentations of practical
applications through case-studies. Bayes linear methods use expectation
as a primitive, which is adjusted in the light of new information.
See our Bayes
linear methods home page for more details.
Data Analysis, Modelling and Simulation (DAMS)
This module is a first course in practical data analysis and computer
modelling. No prior statistical knowledge or computing knowledge
is assumed. The emphasis of the module is upon the understanding
of real-life statistical and mathematical problems, and develops
the basic concepts and methods by example. Most practical sessions
are devoted to computing to apply and illustrate the material presented
The module is designed to be a first statistics course, suitable
for all students satisfying the entrance requirements. No prior
statistical knowledge is assumed. The emphasis is upon the understanding
of real-life statistical problems, and develops the basic concepts
and statistical methods by example. Most practical sessions are
devoted to computing with a statistical package to apply and illustrate
the material presented in lectures.