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 and, briefly, Python. 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:

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

### Syllabus

Introduction and revision - Python and R, and their 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
Independent Study150
Total study time150

Wu, C.F.J. and Hamada, M. (2011). Experiments: planning, analysis and optimisation.

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

Computer requirements. Python and R (freely available)

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

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

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