Study information

Advanced Statistical Modelling - 2021 entry

MODULE TITLEAdvanced Statistical Modelling CREDIT VALUE15
MODULE CODEECM3904 MODULE CONVENERDr Saptarshi Das (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 10
DESCRIPTION - summary of the module content
Statistical modelling lies at the heart of modern data analysis and is a vital part of data science, particularly when decision making is involved. Simple statistical models include linear regression familiar from most foundation courses in statistics. This module places linear regression into the very broad framework of Bayesian statistical data modelling, which has become one of the most popular approaches to data analysis. Bayesian inference will be introduced as a unifying modelling framework, and the module will introduce modelling concepts such as Generalized Linear Models, Generalized Additive Models, Hierarchical Models, Multi-Level Models, Discrete Mixture Models, Models for Flawed Data and predictive model validation. These will provide you with a toolbox and the ability to analyse any real world data set, including binary data, count data, contingency tables, data with temporal and spatial structure as well as data that are missing or partially missing. We will use the statistical software R as the main platform to fit this wide range of models, and will use it in practical sessions so that, as well as a sound theoretical basis, you will develop an understanding of how to apply techniques discussed in the module in practical data analysis.
 
Prerequisite modules: “Statistical Modelling” (ECM2907) and self-learning of bitesize pre-recorded essential material from MTH3041.
 
AIMS - intentions of the module

Statistical data modelling offers a systematic and rigorous way of describing data and thus the mechanisms and processes that generated them. Uncertainty is formally quantified in terms of probability. This module will formally define statistical data modelling as a process by which we can use the data as subjective judgement to construct a mathematical description of the data. It will then argue that Bayesian inference is truly a unifying framework with which we can build and check the validity of statistical data models, while fully quantifying the different sources of uncertainty that result in the apparent haphazard nature of real data sets. The module will introduce well-established but fairly restrictive models such as GLMs but then move on to present more state-of-the-art approaches such as GAMs and Bayesian Hierarchical Models as well as a conceptual framework for correcting flaws in observational data sets (such as censoring). The module will introduce a plethora of real data sets spanning a wide range of applications such as public health, weather, climate, ecology, biology, epidemiology, natural hazards and many others.

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 data structures that can commonly occur and the need to  respect the nature of the data in building statistical models;
 
2 Demonstrate awareness of, and ability to apply, the unifying power and flexibility of  Bayesian inference for data analysis and its use in inference (e.g. quantifying relationships) and prediction;
 
3 Reveal awareness of, and ability to apply, related modern developments in statistical modelling techniques, including nonparametric and semi-parametric formulations (GAMs), Bayesian hierarchical modelling and and models for flawed data;
 
4 Utilise appropriate software and a suitable computer language for advanced modelling of data;
Discipline Specific Skills and Knowledge
 
Discipline Specific Skills and Knowledge
 
5 Demonstrate understanding and appreciation of, and aptitude in, the mathematical definition of stochasticmodels for data perceived to arise at random;
 
6 Apply simulation-based numerical integration methods in the context of Bayesian statistical modelling 
 
7 Appreciate and apply the concept of piecewise processes and their use in semi-parametric statistical models 
 
8 Understanding of the multivariate Normal distribution and its use in Bayesian statistical modelling
 
Personal and Key Transferable / Employment Skills and Knowledge
 
9 Show advanced data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;
 
10 Apply relevant computer software competently;
 
11 Use learning resources appropriately;
 
12 Exemplify self-management and time-management skills;
 
13 Gain experience in problem solving using data analysis.
SYLLABUS PLAN - summary of the structure and academic content of the module
-  Introduction of linear regression as a special case of a statistical model and of statistical modelling as a method;
- Value of  Bayesian inference as a unifying modelling framework;
- Posterior predictive model checking;
- Generalised linear models (GLMs): definition and historical use;
- Generalised additive models (GAMs): definition and a method to capture space-time structures;
- Normal approximation to the posterior and connection to maximum likelihood;
- Hierarchical models: definition and links to random effects and multi-level models;
 - Discrete mixture models and zero-inflation; 
- Models for flawed data.
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled Learning & Teaching activities 33 Lectures/practical classes
Guided Independent Study 33 Post-lecture study and reading
Guided Independent Study 84 Formative and summative coursework 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 1-13 Verbal, in class
Unassessed Practical Modelling Exercises 2 10 hours 1-13 Verbal, in class
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 100 Written Exams 0 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – practical modelling exercises and theoretical 25 10 hours 1-13 Written and oral
Coursework – practical modelling exercises and theoretical problems 1 25 10 hours 1-13 Written and oral
Coursework - project on data analysis 50 20 hours 1-13 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
All above   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
Set Faraway, J.J. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models Chapman & Hall 2006 158488424X
Set A Gelman Bayesian Data Analysis 3rd CRC Press 2013 9781439840955
Set Wood, Simon N. Generalized Additive Models: An Introduction with R Chapman & Hall/CRC 2006 978-1584884743
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM2907
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 6 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 7th May 2015 LAST REVISION DATE Friday 19th March 2021
KEY WORDS SEARCH Generalised Linear Models; Additive Models; Bayesian data analysis; Hierarchical Models; censoring; MCMC.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.