module specification

This module will introduce students to modern statistical modelling techniques and how those techniques  can be used for prediction and forecasting. Throughout the statistical environment  and software R will be used in conjunction with relevant statistical libraries.
The module will,  introduce modern regression techniques (including smoothing),  discuss different model selection techniques (including the classical statistical hypothesis) and  how those techniques can be used for prediction purpose.

1. Introduction to probability, distribution functions and inference
           Different types of probability distribution functions
           Statistical inference and hypothesis testing,

2. Flexible regression models,  for continuous and categorical data including
         i) Generalised Linear Models (GLM)
         ii) Generalised Additive Models (GAM) and
         iii) Generalised Additive Models for Location Scale and Shape (GAMLSS)      
     Introduction to smoothing techniques.

3. Model  selection techniques and forecasting:
        i) Likelihood ratio test 
        ii) Generalised Akaike information criterion
        iii) The bias versus variance dilemma 
        iv) Forward and backward and stepwise selection techniques
        v) ridge regression and lasso
        v) Cross validation techniques 
        vi) Validation and test samples techniques
        vi) Boosting

N/A

On completing the module, students will be able to:

1. Demonstrate substantial knowledge and understanding of modern statistical modelling techniques, and their relation to traditional statistical analyses.

2.  Be able to use R to analyse a wide range of univariate response data, with
     explanatory variates, factors and smoothing.

3. To be able to undestand the different types of density distribution functions, and some of their properties.

4.  To build a statistical model and be able to check its assumptions.

5.  To understand the power and limitation of the prediction (forecasting) techniques .

6. Carry out independent investigation and write clear and concise scientific reports.

7. A critical evaluation and a clear understanding of the applications of legal, social, ethical and professional issues to academic research and PhD programmes.

Due to its practical nature, the module will be assessed by means of a comprehensive case study investigation.  The case study will be based on a realistic data driven problem and will provide an opportunity for students to demonstrate  their skills in problem solving, analysis of data using modern statistical techniques, critical evaluation of selected models and structural report writing ability.

The case study should include:
- Preliminary investigation concerning the problem in hand.
- Selecting suitable methods for solving the problem.
- Evaluating the limitation of the techniques and the impact of any simplifying assumptions on the validity of the solution.
- Gathering input data and using R software for analyses.
- Interpreting the results and writing a comprehensive report of about 5000 words. 
[LO 1-7]

Aitkin M. Francis B. Hinde J. Darnell R. (2009) Statistical modelling in R, Oxford Statistical Science Series 

Hastie T, Tibshirani  R. and Friedman J. (2009) The Elements of statistical Learning. Data Mining, Inference and Prediction. Second Edition, Springer [CORE]

Stasinopoulos D.M. Rigby, R.A. Voudouris V, Heller G. De Bastiani F. (2015) Flexible Regression and Smoothing, The GAMLSS packages in R. First Draft http://www.gamlss.org/wpcontent/uploads/2015/07/FlexibleRegressionAndSmoothingDraft-1.pdf