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Durham University

Department of Mathematical Sciences

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.

Term 1

  • 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.

Term 2

  • 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.

Prerequisites

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

Reading List

Please see the Library Catalogue for the MATH3051 reading list.

Examination Information

For information about use of calculators and dictionaries in exams please see the Examination Information page in the Degree Programme Handbook.