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School of Mathematics

# MATH38092 - 2007/2008

General Information
• Title: Practical Statistics 2
• Unit code: MATH38092
• Credits: 10
• Prerequisites: MATH10401, MATH20701, MATH20812 Practical Statistics 1, MATH38011 Linear Statistical Models. Any students who have with to take this unit but did not take MATH38011 should contact the lecturer for advice on necessary preliminary reading.
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible:
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## Specification

### Aims

To teach practical aspects of statistical modelling and inference at the third year level.

### Brief Description of the unit

This 10-credit unit teaches the practical aspects of statistical modelling and inference at the third year level. It begins with maximum likelihood, and the rest of the unit follow this theme. The statistical package S-PLUS will be used whenever appropriate.

### Learning Outcomes

On successful completion of this course unit students will

• be able to fit certain distributions or models by maximum likelihood;
• be able to check model adequacy and make inferences, and
• have experience of writing statistical reports.

### Future topics requiring this course unit

MATH48121 Computationally Intensive Statistics

### Syllabus

1. Introduction to (or revision of) S-PLUS. [2]
2. Maximum likelihood estimation: normal equations, Newton-Raphson algorithm, Fisher's information and asymptotic normality (no proof), likelihood-ratio tests. Project 1. [4]
3. Nonlinear regression: model specification, least squares estimation, Gauss-Newton algorithm and its modifications, residual analysis, inferences. Project 2. [4]
4. ARMA models: model specification, causality and invertibility conditions, estimation of parameters by maximum likelihood, choosing model by AIC/BIC, prediction. Project 3. [4]
5. Kernel density estimation and classification: the histogram, kernel smoothing, choice of bandwidth, classification, maximum likelihood rule. Project 4. [4]
6. Gaussian mixtures and clustering. Project 5. [4]

### Textbooks

• W N Venables and B D Ripley, Modern Applied Statistics with S, 4th ed., Springer-Verlag 2002.

### Teaching and learning methods

Two lectures and one computer class each week. In addition students should expect to spend at least four hours each week on private study for this course unit.

### Assessment

Coursework: choice of four projecs from five offered 100%

## Arrangements

On-line coures materials for this course unit.