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:

Construct models and predictions that can be expected to have good statistical properties, based on exploring alternative models and using cross-validation.
- Formulate statistical models and estimate their parameters. Interpret the estimated model.
- 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
Teaching	16
Independent Study	59
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.