Advanced Statistical Modelling - 2019 entry

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).

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.

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

Module Specific Skills and Knowledge

Discipline Specific Skills and Knowledge

Personal and Key Transferable / Employment Skills and Knowledge

- 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;

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.

Basic reading:

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

Web based and Electronic Resources:

Other Resources:

Reading list for this module: