Final year undergraduate courses; brief descriptions
All these courses consist of about 38 lectures (45 minutes), 2 per week during the first (October-December)
and second term (January-March).
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.
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.
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
problems.
The course starts with an introduction to the ideas of decision analysis and the use
of decision trees. The use of influence diagrams to represent decision problems is explained.
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.
Probability III/IV
While many aspects of the future are unpredictable, one may hope to
be able to quantify this unpredictability.
The mathematical theory of probability aims to build a
formal logical structure on this intuition.
This course builds on an introductory (first-year) course in probability, and should appeal
to students interested in the mathematical theory underlying much of statistics. Topics from
classical probability theory that are covered include the Strong Law of Large Numbers and the
Central Limit Theorem, as well as more modern topics such as martingale theory. Some applications
of the theory are discussed, for example in mathematical finance and in engineering.
Stochastic Processes III/IV
Many systems in e.g. the physical sciences, biology, economics, engineering and computer sciences may
best be modelled by stochastic processes. These are collections 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 covered in this course include Markov chains in
discrete and continuous time, Poisson processes and Gaussian processes.
Operations Research III
This course introduces some methods in mathematical Operations Research, for example linear
programming (simplex method) with applications, inventory theory (both deterministic and stochastic),
dynamic programming, Markov decision processes and nonlinear programming. The course has an introductory
nature, with emphasis on examples considering applications.
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Frank Coolen
Last revision: 3/10/98