# Mathematics

## ECM3712 - Advanced Statistical Modelling (2015)

MODULE TITLE CREDIT VALUE Advanced Statistical Modelling 15 ECM3712 Prof Trevor Bailey (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
 Number of Students Taking Module (anticipated) 28
DESCRIPTION - summary of the module content

Statistical modelling lies at the heart of modern data analysis. A statistical model is the specification of a joint probability distribution for the response variable (or variables) in the data. It also includes mathematical relationships between key characteristics of that probability distribution and other explanatory variables present in the data. Simple statistical models include the techniques of regression and multiple regression familiar from most foundation courses in statistics. This module takes those ideas further placing them in the much broader context of the generalised linear model. It then goes on to consider extensions to that framework involving random effects, generalised linear mixed models, additive models and Bayesian approaches to statistical modeling. We will discuss software currently in use to fit this wide range of models, and will use it in the lab so that, as well as a sound theoretical basis, you will develop an understanding of how to apply techniques discussed in the course in practical data analysis.

Pre-requisite: ECM2710 or equivalent

AIMS - intentions of the module

The introduction of generalised linear models (GLMs) by Nelder and Wedderburn in 1972 was a milestone in statistical modelling. It provided a unified framework for many seemingly unrelated data analysis techniques. This module will describe the underlying theory and give you a general introduction to the application of commonly used GLMs. The module then goes on to discuss related developments in modern statistical modelling, including nonparametric and semi-parametric formulations (GAMs), hierarchical modelling and random effects (GLMMs), and Bayesian approaches to statistical modelling.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 show understanding of the many different types of statistical data structure that commonly occur and the need to model relationships in such data appropriately;
2 demonstrate awareness of, and ability to apply, the unifying power and flexibility of the generalised linear model (GLM) as a means of describing relationships in data;
3 reveal awareness of, and ability to apply, related modern developments in statistical modelling techniques, including nonparametric and semi-parametric formulations (GAMs), hierarchical modelling and random effects (GLMMs) and Bayesian approaches to statistical modeling;
4 utilise appropriate software and a suitable computer language for advanced modelling of data.
Discipline Specific Skills and Knowledge:
5 demonstrate understanding and appreciation of, and aptitude in, the advanced mathematical modelling of stochastic phenomena and its usefulness;
Personal and Key Transferable/ Employment Skills and  Knowledge:
6 show advanced data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;
7 apply relevant computer software competently;
8 use learning resources appropriately;
9 exemplify self management and time-management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

- introduction to advanced statistical modelling of relationships between variables: the need to move beyond the normal theory linear model (motivation and examples);
- value of general modelling frameworks and paradigms;
- generalised linear models (GLMs): definition, maximum likelihood estimation, iteratively reweighted least squares, inference in the GLM, GLM selection, GLM diagnostics;
- examples of GLMs, normal linear models as GLMs, Bernoulli and binomial data, Poisson count data, contingency tables, multinomial data, other GLMs, mean dispersion relationships and overdispersion, quasi-likelihood;
- generalised additive models (GAMs): parametric versus nonparametric and semi-parametric models, kernel, spline and local polynomial estimation methods, additive models and generalized additive models;
- hierarchical models and random effects: the whats and whys of random effects and hierarchical (multilevel) modelling, normal theory linear mixed models, generalised linear mixed models (GLMMs);
- Bayesian modelling methods: motivation, the Bayesian modelling framework, inference and Bayesian modelling, MCMC fitting techniques, Metropolis-Hastings and Gibbs sampling, examples of Bayesian models (GLMMs, and beyond).

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 33 117
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures/practical classes Guided independent study 33 Post lecture study and reading Guided independent study 40 Formative and summative coursework preparation Guided independent study 44 Exam revision/preparation

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Unassessed practical modelling exercises 1 10 hours 1, 2, 4-9 Verbal, in class
Unassessed practical modelling exercises 2 10 hours 1, 3, 4-9 Verbal, in class

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 30 70
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 70 2 hours 1-6, 9 Verbal on specific request
Coursework – practical modelling exercises and theoretical problems 1 15 10 hours 1, 2, 4-9 Written and verbal
Coursework – practical modelling exercises and theoretical problems 2 15 10 hours 1, 3, 4-9 Written and verbal

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Type Author Title Edition Publisher Year ISBN Search
Set Congdon, P. Bayesian Statistical Modelling Wiley 2001 047-1496006 [Library]
Set Krzanowski W.J. An Introduction to Statistical Modelling Arnold 1998 000-0-340-69185-9 [Library]
Set Aitkin, M., Francis, B., Hinde, J. and Darnell, R. Statistical Modelling in R Oxford University Press 2008 9780199219131 [Library]
Set Congdon, P. Applied Bayesian Modelling Wiley 2003 047-1486957 [Library]
Set Faraway J J Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models Chapman & Hall 2006 158488424X [Library]
Set Crawley, M.J. The R Book Wiley 2007 9780470510247 [Library]
Set Wood, Simon N Generalized additive models: an introduction with R Chapman & Hall/CRC 2006 978-1584884743 [Library]
Set Brooks, S, Gelman, A, Jones, G et al Handbook of Markov Chain Monte Carlo Chapman & Hall/CRC 2011 978-1420079418 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM2710
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Friday 09 January 2015 Wednesday 11 March 2015
KEY WORDS SEARCH Generalised linear models; mixed models; additive models; Bayesian modelling.