MATH6112 Computer-based statistical modelling

Module Overview

The aim of the course is to provide a modern view of computer-based data analysis, from the statistical point of view. The course is intended for students with a solid basic background in probability, statistical methods, and computing, and who aim to build on this background. Topics are covered at a brisk pace; to make the best of this course, students can expect to put in significant self-study.

Aims and Objectives

Module Aims

The overarching aim of the course is to provide the student with modern view of computer-based data analysis, from the statistical point of view. The course gives a unified and comprehensive approach to the subject.

Learning Outcomes

Having successfully completed this module you will be able to:

- Formulate statistical models and estimate their parameters. Interpret the estimated model.
Construct models and predictions that can be expected to have good statistical properties, based on exploring alternative models and using cross-validation.
- Produce a technical report that describes problem formulation and solution

Syllabus

- Revision of probability essentials - Introduce maximum-likelihood estimation and develop it for selected parametric models such as independent sampling and regression, including generalized linear models. Develop confidence intervals and hypothesis tests via the asymptotic normality result - Introduce optimal statistical decisions. Define a loss function and develop optimal binary classification as the main example. - Selected topics in model selection. In-sample and out-of-sample error. Cross-validation for model selection.

Learning and Teaching

Teaching and learning methods

A range of teaching and learning methods is used, centered on lectures, computer laboratories, and private study.

Type	Hours
Independent Study	59
Teaching	16
Total study time	75

Resources & Reading list

Hastie, T and R. Tibshirani and J. Friedman (2009). The elements of statistical learning.

Assessment

Summative

Method	Percentage contribution
Coursework assignment(s)	100%

Repeat

Method	Percentage contribution
Coursework assignment(s)	100%

Referral

Method	Percentage contribution
Coursework assignment(s)	100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisites: - MATH1024 and MATH2010 or equivalent maturity with Probability and Statistics - Basic familiarity with programming in matlab or R or equivalent.