The University of Southampton
Courses

MATH6157 Applied Statistical Modelling

Module Overview

This module will introduce important general aspects of statistical modelling and some fundamental aspects of data collection for computer and simulation experiments. A broad range of commonly-used statistical models will be encountered, and used to demonstrate both general principles and specific examples of modelling techniques in R. A variety of exemplar applications and data sets will be presented.

Aims and Objectives

Module Aims

To introduce, via a hands-on approach, the basic concepts and principals in statistical modelling in a computational paradigm.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• understand how to use R to fit, explore and exploit a variety of statistical models
• should understand why statistical modelling is important
• demonstrate an ability to concisely convey technical results
• understand the terminology and statistical principles associated with modelling
• understand sufficient theory to deal with simple examples and have gained practical hands-on experience in more complex examples

Syllabus

Introduction and revision - R, and its interface - Data input, plotting and summaries - Standard statistical distributions - Principles of statistical inference - Likelihood Regression: linear and generalised linear modelling - Model construction and estimation - Model selection and information criteria - Shrinkage regression (Lasso and ridge methods) Random effects, mixed models, and data with complex correlation structures - Grouping structures in data - Interpretation of random effects and mixed models - Discrete data and generalised linear mixed models - Estimation of mixed models - Autoregression models Smoothing and nonparametric regression - Kernel density estimation - Splines and penalised splines - Generalised additive models - Linear smoothing Data collection for computational studies - Fundamentals of design of experiments - Computer and simulation experiments - Latin hypercube sampling

Learning and Teaching

Teaching and learning methods

Teaching methods - 24 lecture hours - 24 computer workshop hours Learning methods - Individual study facilitated via weekly worksheets to support lecture material and assessed coursework - Supervised problem solving via computer lab sessions

TypeHours
Teaching48
Independent Study102
Total study time150

Computer requirements. R (freely available)

Faraway, J.J. (2016). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models.

Davison, A.C. (2008). Statistical Models.

Wood, S.N. (2006). Generalized Additive Models: An Introduction with R..

Gelman, A. and Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models.

Wu, C.F.J. and Hamada, M. (2011). Experiments: Planning, Analysis and Optimisation.

Faraway, J. (2014). Linear Models with R.

Assessment

Summative

MethodPercentage contribution
Class Test 50%
Class Test 50%

Referral

MethodPercentage contribution
Coursework assignment(s) 100%

Repeat Information

Repeat type: Internal & External