MATH3051 Statistical Methods III
The course introduces widely used statistical methods. The course 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. Having a particular emphasis on the intersection of theory and practice, the learning objective of the course includes the ability of performing hands-on data analysis using the statistical programming language R. Therefore, four computer practicals will be held in each of Michaelmas and Epiphany term. Towards the end of each term, a practical examination component will be held, each of which contributes 15% towards the total examination mark.
Topics include: statistical computing using R; multivariate analysis (in particular, principal component analysis); regression (linear model: inference, prediction, variable selection, influence, diagnostics, outliers); analysis of designed experiments (analysis of variance); extensions to transformed, weighted, and/or nonparametric regression models.
There is not one recommended book but the books in the reading list more than cover the course material; in particular those by Weisberg and Krzanowski provide (in conjunction) a good coverage in an accessible style. The book by Kutner et al. is quite voluminous but worth of consideration for those who prefer a detailed step-by-step description of the methods.
Outline of Course
Aim: To provide a working knowledge of the theory, computation and practice of statistical methods, with focus on the linear model.
- Basics: Statistical computing in R, matrix algebra, multivariate probability and likelihood, multivariate normal distribution.
- The linear model: Assumptions, estimation, inference, prediction, analysis of variance, designed experiments, model selection.
- Regression diagnostics: influence, outliers, lack-of-fit.
- Introduction to multivariate analysis: Variance matrix estimation, Mahalanobis distance, principal component analysis; dimension reduction.
- Extensions: Basics of transformed, weighted, and/or nonparametric regression models.
For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook.
Please see the Library Catalogue for the MATH3051 reading list.