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School of Mathematics

# MATH38092 - 2008/2009

General Information
• Title: Practical Statistics 2
• Unit code: MATH38092
• Credits: 10
• Prerequisites: MATH20802 Statistical Methods , MATH20812 Practical Statistics 1, MATH38011 Linear Statistical Models,
• 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 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, prediction. Project 2. [6]
4. Time Series Regression : serially correlated errors, the acf and pacf , identification of correlation structure, maximum likelihood estimation using gls in S-Plus. 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. the EM algorithm, clustering. [2]

### Textbooks

• W N Venables and B D Ripley, Modern Applied Statistics with S, 4th ed., Springer-Verlag 2002.
• M J Crawley, Statistical Computing - An Introduction to Data Analysis using S-Plus, John Wiley 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: four projects (80%) plus coursework tests (20%)

## Arrangements

On-line course materials for this course unit.