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Department of Mathematical Sciences

MATH3361/4071 Topics in Statistics III/IV

The module presents a number of widely used statistical methods, some building on material in Statistical Concepts II and others on material in Statistical Methods III which is a pre-/co-requisite.

The module should be of particular interest to those who intend to follow a career in statistics or who might choose to do a fourth year project in statistics. It is intended to broaden the range of contexts in which you will be able to function as a statistician and to build upon the linear model intuition developed in Statistical Methods III.

Key topics are: the generally applicable method of maximum likelihood estimation in the context of models with multiple parameters; contingency table analysis which nicely complements the material on modelling continuous variables in Statistical Methods III; generalized linear models which extend the linear model ideas in Statistical Methods III to a wide class of data scenarios. This includes regression problems with categorical response, as used for instance in the banking sector for credit scoring. Time permitting, an advanced topic will be studied towards the end of the course.

Outline of Course

Aim: To provide a working knowledge of the theory, computation and practice of a variety of widely used statistical methods.

Term 1

• Likelihood estimation: Likelihood and score functions for multi-parameter models, Fisher information, confidence regions, method of support, likelihood ratio tests, profile likelihood, Akaike and Bayes information criteria (AIC & BIC).
• Contingency tables: Sampling models, log-linear modelling, iterative proportional fitting, model selection, goodness of fit.

Term 2

• Generalised linear models: Framework, exponential families, likelihood and deviance, standard errors and confidence intervals, prediction, analysis of deviance, residuals, over-dispersion.
• Advanced topic: One of multivariate analysis, time series analysis, or medical statistics.

Prerequisites

For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook: MATH3361, MATH4071.