Mathematics (Penryn)

ECM3904 - Advanced Statistical Modelling (2018)

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MODULE TITLEAdvanced Statistical Modelling CREDIT VALUE15
MODULE CODEECM3904 MODULE CONVENERProf Gavin Shaddick (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 40
DESCRIPTION - summary of the module content

Often real-world measurements deviate from an assumption of normality. The field of Generalised Linear Modelling extends the theory of multiple regression to deal with non-normal error structures, and thus provides a flexible technique that can be used to model a wide range of real-world processes. In addition, the assumption that observed data are independent is often untrue, and so we explore ways in which generalized linear models can be extended to deal with correlated data (through the use of mixed effects models).

Furthermore, the task of inferring physical, ecological and biological processes from observed data is made more challenging in systems with hidden processes and/or missing data. The Bayesian framework provides a powerful means for overcoming some of these challenges, and can often deal with systems where classical statistical methods fail. Although Bayes' Theorem has existed since the late 18th century, it was not until the availability of cheap computing power in the latter part of the 20th century that Bayesian methods were able to be widely adopted and implemented, and they now form the cornerstone of many emerging methodologies in fields such as bioinformatics, data mining, machine learning, epidemiology and ecology, engineering, medicine, finance and law.

In this module you will learn the principles of Generalised Linear Modelling, Mixed Models and Bayesian analysis, and the philosophical comparisons of the latter to classical statistical methods. You will learn about common numerical techniques for model fitting, and how to apply these in various open source software packages.

Prerequisite modules: “Probability and Statistics” (ECM1909) and “Statistical Modelling” (ECM2907).

AIMS - intentions of the module

This module aims to lay the foundations for a thorough understanding of modern Bayesian theory and practice. It aims to provide the practical skills required for students to analyse and present data effectively, how to develop and fit models in the Bayesian framework, and how to interpret and disseminate the results from a Bayesian analysis. The module also aims to highlight and discuss the differences between frequentist and Bayesian philosophies.

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 understand the theory underlying the use of Generalised Linear Models, and how these relate to standard normal regression;
2 understand the fundamental concepts of modern Bayesian theory, and how these contrast to the classical framework;
3 demonstrate knowledge of the processes involved in developing statistical models in general, as well as within the Bayesian paradigm;
4 understand and apply these advanced methods in a range of practical applications;
5 develop knowledge in model building, validation and comparison;
6 apply these ideas in practice to real data using open source software such as R;

Discipline Specific Skills and Knowledge

7 demonstrate a clear understanding of fundamental concepts, and how they relate to traditional methods.  These include the notions of uncertainty and evidence, and the processes involved in designing, checking and refining statistical models, including the limitations of the approaches and how these impact inference;
8 improve computational skills in R, and gain a better understanding of the practical implementation of these approaches;

Personal and Key Transferable / Employment Skills and Knowledge

9 demonstrate key data analysis skills, including the practical implementation in R;
10 formulate and solve problems and communicate reasoning and solutions effectively in writing;
11 demonstrate appropriate use of learning resources;
12 demonstrate self management and time management skills.

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

- Introduction to Generalised Linear Modelling and review of likelihood theory;

- Review of probability distributions, including the concepts of joint, marginal and conditional distributions, expectations and higher moments;

- Non-independence and the use of mixed models;

- Bayes' Theorem and Bayesian inference;

- Prior distributions;

- Point and interval estimation;

- Markov chain Monte Carlo (MCMC);

- Hierarchical models and their link to classic random effects models;

- Model checking and validation;

- Bayesian model choice;

- Data augmentation and reversible jump MCMC;

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 49.00 Guided Independent Study 101.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled Learning & Teaching activities 33 Formal lectures of new material
Scheduled Learning & Teaching activities 16 Computer classes and tutorials
Guided Independent Study 101 Lecture & assessment preparation, wider reading

 

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
Fortnightly exercise 10 hours 1-12 Feedback given on questions during tutorials and detailed model answers.
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 40 Written Exams 60 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
2 x Coursework - based on the skills learned in the formative assessment papers, and the R practical classes 20 each 2 x 10 hours 1-12 Written and oral
Written exam – closed book 60 1.5 hours 1-12 Written and oral
         
         
         

 

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-assessment
Coursework Written Exam All August Ref/Def Period
Written exam Written Exam 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

Basic reading:

 

ELE: http://vle.exeter.ac.uk

 

Web based and Electronic Resources:

 

Other Resources:

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set A Gelman Bayesian Data Analysis 3rd CRC Press 2013 9781439840955 [Library]
Set Gamerman D. & Lopes F.H. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference 2nd Chapman & Hall 2006 978-1584885870 [Library]
Set McCullagh P. & Nelder J. Generalized Linear Models 2nd Chapman & Hall 1989 000-0-412-31760-5 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM1909, ECM2907
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 6 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 07 May 2015 LAST REVISION DATE Friday 10 August 2018
KEY WORDS SEARCH Statistics; Bayesian; hierarchical models, Markov chain Monte Carlo; inference.