# 2022/23 Taught Postgraduate Module Catalogue

## MATH5741M Statistical Theory and Methods

### 15 creditsClass Size: 127

Module manager: Dr Benjamin Thorpe
Email: b.thorpe@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### This module is mutually exclusive with

 MATH3723 Statistical Theory

This module is not approved as an Elective

### Module summary

This module gives an introduction to the basics of statistics, aimed at students who did not take any statistics modules during their undergraduate degree.

### Objectives

The objective of the module is to give a general unified theory and method of estimation and hypotheses testing, and to introduce Bayesian inference and the comparison with classical inference.

Learning outcomes
On completion of the module, a student should:
- be able explain the role of statistical models;
- be able to compute statistical estimators and to assess the estimation error;
- be able to perform simple statistical tests and to interpret the results;
- understand the interplay of prior information and data in Bayesian inference.

### Syllabus

Syllabus:
- the role of statistical models;
- statistical estimators, bias, mean squared error (MSE);
- standard examples of estimators (e.g. sample mean, sample variance);
- computing estimators in R;
- the effects of sample size and of outliers;
- statistical tests, error probabilities;
- standard examples of tests (e.g. t-test);
- performing tests in R;
- Bayesian inference, Bayes' rule, prior/posterior distribution.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Practical 11 1.00 11.00 Private study hours 117.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 150.00

### Private study

The student will be expected to complete regular written worksheet assignments testing their understanding of theoretical course elements.

Using the statistical software R, the student will learn to compute estimates, their standard error, bias, mean square error, to understand the effect of sample size and outliers, and to perform hypothesis tests and inference both in the classical and Bayesian context. Part of the assessment for the module consists of a practical, where the student will apply these techniques to a real-world data set.

### Opportunities for Formative Feedback

Monitoring by regular worksheets and achievement in supervised practical sessions.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Practical Report 20.00 Total percentage (Assessment Coursework) 20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated