Statistical Models and Methods

Code

MATH2047

School

Mathematical Sciences

Level

2

Credits

20

Semesters

Full Year Malaysia

Summary

The first part of this course provides an introduction to statistical concepts and methods. A wide range of statistical models will be introduced to provide an appreciation of the scope of the subject and to demonstrate the central role of parametric statistical models. The key concepts of inference including estimation and hypothesis testing will be described. Special emphasis will be placed on maximum likelihood estimation and likelihood ratio tests. While numerical examples and computer lab sessions will be used to motivate and illustrate, the content will emphasise the mathematical basis of statistics. Topics include maximum likelihood estimation, confidence intervals, likelihood ratio tests, categorical data analysis and non-parametric procedures.
The second part of the course introduces a wide class of techniques such as regression, analysis of variance, analysis of covariance and experimental design which are used in a variety of quantitative subjects. Topics covered include the general linear model, least squares estimation, normal linear models, simple and multiple regression, practical data analysis, and assessment of model adequacy. As well as developing the theory, practical experience will be obtained by the use of a statistical computer package.

Target Students

Single Honours and Joint Honours from the School of Mathematical Sciences

Co-requisites

Modules you must take in the same academic year, or have taken in a previous year, to enrol in this module:

• Probability Models and Methods (MATH2046)

Classes

• One 1-hour tutorial each week for 18 weeks
• One 2-hour lecture each week for 24 weeks
• One 1-hour computing each week for 6 weeks

Assessment

• 15% Coursework 1: Advanced take-home exercise on statistical data analysis and hypotheses tests using software packages (end spring semester).
• 10% In-class Exam 1: Inclass test (Autumn)
• 75% Exam 1 (3-hour): 3 hours written examination

Educational Aims

Learning Outcomes

A student who completes this module successfully will be able to:

L1 - apply methods concerning estimation of parameters in standardstatistical models; in particular the method of moments and the maximum likelihood method;

L2 - apply methods for interval estimation; in particular, exact and approximate confidence intervals based on asymptotic theory;

L3 - perform statistical hypotheses tests using data from studies (such as t and F-tests, comparison of models and parameter values);

L4 - apply methods for analysing categorical data and methods without having to make distributional assumptions (non-parametric statistics);

L5 - fit a linear model to data, both manually and using statistical software;

L6 - check model fit, diagnose errors, and perform model selection amongst the class of linear models.

Conveners

• Shin Zhu Sim