Number of lectures per week: 3
End-of-year Examination: One 3-hour examination
Description: Statistics is concerned with studying uncertainty in many guises. In recent years there has been a growth in the number of methods available. Many of these methods of analysis were very difficult or impossible to implement in the past, but with the recent increase in computational power, these are now possible.
Applications of these methods are now commonly found in actuarial studies, financial statistics, risk analysis, medical statistics, and the physical sciences.
This course will give an overview of many of these statistical methods. The theory behind the methods will be covered as well as the implementation of these methods. The comparison of the various methods will be emphasised.
While the methods covered in this course require a significant amount of computer involvement in practice, the emphasis of the course will be on the theoretical background, and algorithms for implementation rather than any specific computer coding or package. Some specific software will be mentioned, and students will have the opportunity to refer to these, should they so wish.
Topics covered may include:
Likelihood based methods
Generalized Linear Models
Generalized Additive Models
Non-parametric regression and smoothing
The Bootstrap, Jacknife and other resampling methods
The EM Algorithm and Data Augmentation
Markov Chain Monte Carlo Methods
Maximum Entropy Methods
Dobson, A. (1990) Introduction to Generalized Linear Models. Chapman & Hall.
Efron, B. and Tibshirani, R. (1994) An Introduction to The Bootstrap. Chapman & Hall.
Ferguson, T. (1996) A Course in Large Sample Theory. Chapman & Hall.
Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. Chapman & Hall.
McCullagh, P. and Nelder, J. (1989) Generalized Linear Models. Chapman & Hall.
Sivia, D. (1996) Data Analysis: A Bayesian Tutorial. Oxford.
Tanner, M. (1997) Tools for Statistical Inference. Springer-Verlag.
Venables, W. and Ripley, B. (2000) Modern Applied Statistics with S-Plus. Springer-Verlag.
Oct 17, 2000