The University of Southampton
Courses

# MATH6153 Statistical Theory and Linear Models

## Module Overview

This module provides an intensive introduction to, or revision of, essential ideas in developing statistical theory. Firstly, common statistical models are reviewed along with their theoretical properties. Then the transformation method for random variables is introduced to derive three standard statistical distributions. The middle part of the module concerns the theory for making statistical inference, including methods such as maximum likelihood estimation and likelihood ratio tests, and an introduction to Bayesian methods. Finally, the theory of least squares methods for linear models is introduced.

### Aims and Objectives

#### Module Aims

• Standard univariate statistical models and their properties. • Theory of estimation and significance testing. • Bayesian inference and prediction methods for conjugate priors. • Theory of linear statistical models.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• demonstrate a very good understanding of standard univariate statistical models and their properties. demonstrate a very good understanding of the theory of estimation and hypothesis testing. demonstrate a very good understanding of Bayesian inference and prediction methods using conjugate prior distributions. demonstrate a very good understanding of the theory of linear models.

### Syllabus

• Univariate distributions: Common standard distributions and their properties. • Estimation: Unbiasedness, Method of Moments, • Likelihood - score functions, information, maximum likelihood estimators, Cramer-Rao lower bound • Confidence intervals: Asymptotic methods and interpretations. • Hypothesis testing: Neyman-Pearson Lemma and the Generalised likelihood ratio tests. • Bayesian inference and prediction methods using conjugate prior distributions. • Theory of linear models: o Simple and multiple linear regression, o The principle of least squares and least squares estimators, o Linear hypothesis testing, o Properties of least squares estimators, o Model selection.

### Learning and Teaching

#### Teaching and learning methods

36 Lectures and 12 Tutorials

TypeHours
Independent Study152
Teaching48
Total study time200

Braun, W.J. and Murdoch, D.J (2007). A First course in Statistical Programming with R..

MH DeGroot & MJ Schervish (2001). Probability and Statistics.

Hannelore Liero and Silvelyn Zwanzig (2012). Introduction to the Theory of Statistical Inference.

Statistical Inference (1990). G Casella & RL Berger.

### Assessment

#### Assessment Strategy

The assessment for the repeat candidates will be based completely on the final examination.

#### Summative

MethodPercentage contribution
Coursework 30%
Exam 70%

#### Referral

MethodPercentage contribution
Exam  ( hours) 100%

#### Repeat Information

Repeat type: Internal & External

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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