The University of Southampton
Mathematical SciencesPostgraduate study

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 Python and R. A variety of exemplar applications and data sets will be presented.

Aims and Objectives

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

After taking this module, students should understand

  • why statistical modelling is important,
  • the terminology and statistical principles associated with modelling,
  • sufficient theory to deal with simple examples and have gained practical hands-on experience in more complex examples,
  • how to use Python and R to fit, explore and exploit a variety of statistical models

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

Study time allocation

Contact hours:60
Private study hours:90
Total study time: 150 hours

Teaching and learning methods

Teaching methods

  • 24 lecture hours
  • 36 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

Resources and reading list

For resources which are required or considered useful for the module: key texts, text books, data books, software, web sites, other sources of related information.

Description and/or list, with URL, library reference, etc

Software: Python and R (freely available)

Textbooks: no required textbooks but the following texts are considered useful:

  • Davison, A.C. (2008). Statistical Models. CUP (QA 276 DAV).
  • Faraway, J. (2014). Linear Models with R, (2nd Edn). Chapman and Hall/CRC (QA 279 FAR).
  • Gelman, A. and Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. CUP (HA 31.3 GEL).
  • Wood, S.N. (2006). Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC (QA 274.73 WOO).
  • Wu, C.F.J. and Hamada, M. (2011). Experiments: planning, analysis and optimisation, (2nd Edn). Wiley (QA 279 WU).

Assessment

Assessment methods

Assessment Method Number % contribution to final mark Final assessment (x)
Coursework (formative and summative) 2 100% (50% each) x
Feedback Method      
Verbal feedback on (unassessed) worksheets and exercises in lab sessions
Written feedback on both assessed pieces of coursework
     
Referral Method Number   % contribution to final mark  
Repeat a suitable modified piece of coursework 1 100%  

Method of repeat year: Repeat year internally or externally

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