School of Mathematics and Statistics

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2011/2012 Sem. 1

Aims

- To demonstrate the power and elegance of unifying a large number of simple statistical models within the framework of the generalised linear model.

- To train a student in the interpretation, analysis and reporting of data, when a single response measurement is to be interpreted in terms of one or a number of other variables and factors.

Objectives

By the end of the course students are expected to:

- be able to formulate appropriate problems as generalised linear models;

- understand and prove the basic properties of least squares estimators;

- understand the assumption of the models and be able to test these;

- understand the distribution results that allow competing models to be compared;

- carry out exploratory and confirmatory analyses using R;

- write a comprehensible report describing the analysis of a data set and the conclusions which can validly be drawn from it;

- interpret and criticise R analyses of data .

Syllabus

Generalised linear models, and ordinary linear models.
How to build models (with design matrices).
The exponential family of distributions (Normal, binomial, Poisson etc.).
Checking models: residuals etc.
How GLMs are fitted to data.
Dealing with overparameterized models.
Inference (sampling distribution of parameters and analysis of deviance).
Models for contingency tables (and why the canonical link is interesting).
The geometry of least squares and orthogonality.
Projectors, sums of squares and ANOVA.
Gauss-Markov Theorem.
Transformation theory.

Textbooks

An Introduction to Statistical Modelling: W Krzanowski, Arnold.
An Introduction to Generalized Linear Models: A J Dobson, Chapman & Hall.

Assessment

Project = 20%, 2 Hour Examination = 80%

Prerequisites

MT2004 and MT3501 (as co-requisite)

MT5753

Availability

Academic year 2012/13 in semester 1 at 9

Dr A Overstall