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.

Pre-requisite Modules: MTH2006 or equivalent (knowledge of linear regression) and MTH3041 or equivalent (e.g. self-learning of bitesize pre-recorded essential material from MTH3041)
 

 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.

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 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 (GLMs): 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.
 

Reassessment will be by coursework in the failed or deferred element only. For referred candidates, the module mark will be capped at 40%. For deferred candidates, the module mark will be uncapped.

Reading list for this module: