The University of Southampton
Courses

# MATH6165 Statistical Theory for Data Scientists

## Module Overview

This module provides an introduction to essential ideas in statistical theory. Firstly, basic statistical models are reviewed along with their properties. Then the transformation method for random variables is introduced to derive standard statistical distributions. The final 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.

### Aims and Objectives

#### Module Aims

The aims of the module are: • Standard univariate statistical models and their properties. • Theory of estimation and significance testing, and know when particular tests should be applied. • Bayesian inference methods for conjugate priors, prediction method and marginal likelihood.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• demonstrate a good understanding of standard univariate statistical models and their properties.
• demonstrate a good understanding of the theory of estimation and significance testing, and know when particular tests should be applied.
• demonstrate a good understanding of Bayesian inference methods for conjugate prior, prediction method and marginal likelihood.

### Syllabus

• Univariate distributions: Common standard distributions and their properties. • Estimation: Unbiasedness, Method of Moments, • Likelihood - score functions, information, maximum likelihood estimators, Cramer-Rao • Inequality. • Confidence intervals: Asymptotic methods and interpretations. • Hypothesis testing: Neyman-Pearson Lemma and the Generalised likelihood ratio tests. • Bayesian methods for conjugate priors, prediction method and marginal likelihood.

### Learning and Teaching

#### Teaching and learning methods

27 Lectures and 9 Tutorials

TypeHours
Tutorial9
Follow-up work8
Preparation for scheduled sessions8
Revision10
Lecture27
Total study time77

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

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

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

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

### Assessment

#### Summative

MethodPercentage contribution
Coursework 30%
Exam  (2 hours) 70%

#### Referral

MethodPercentage contribution
Exam  (2 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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