Postgraduate Course: Likelihood and Generalized Linear Models (MATH11121)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  The concept of likelihood is central to statistical inference. This course develops likelihood methods for single parameter and multiparameter problems, including iterative maximum likelihood estimation, likelihoodbased confidence regions and likelihood ratio tests.
An important application of likelihood methods is to generalized linear models which provide a broad framework for statistical modelling of discrete or continuous data. Special cases of such models are considered. 
Course description 
This syllabus is for guidance purposes only :
1. Statistical modelling and applications of likelihood.
2. Likelihood principles.
3. Likelihood based inference for single parameter and multiparameter models.
4. Wald, score, and likelihood ratio tests and related confidence regions.
5. Generalized likelihood ratio tests.
6. Applied aspects of maximum likelihood estimation, including graphical approaches, iterative estimation and the method of scoring.
7. Statistical modelling using generalized linear models, link functions and exponential family distributions.
8. Several examples of generalized linear models, including normal, Poisson, exponential, gamma and binary regression.
9. Diagnostic and residual analyses for generalized linear models.
10. Using R to fit and assess models.

Course Delivery Information
Not being delivered 
Learning Outcomes
1. Familiarity with a wide range of statistical modelling situations.
2. Ability to apply likelihood based inference to real modelling situations.
3. Ability to apply likelihood methods to derive estimates, confidence regions and hypothesis tests.
4. Familiarity with examples of generalized linear models.
5. Ability to use R for statistical modelling and data analysis.
6. Ability to analyse data and interpret results of statistical analyses.

Reading List
1. Azzalini, A., (1996). Statistical Inference Based on the Likelihood. Chapman & Hall, London.
2. Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference using Likelihood. Oxford University Press, Oxford.
3. Dobson, A.J. (2002). An Introduction to Generalized Linear Models, 2nd Edition. Chapman & Hall/CRC, London.
4. McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models, 2nd Edition. Chapman & Hall, London. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  LGLM 
Contacts
Course organiser  Dr Bruce Worton
Tel: (0131 6)50 4884
Email: Bruce.Worton@ed.ac.uk 
Course secretary  Mrs Frances Reid
Tel: (0131 6)50 4883
Email: f.c.reid@ed.ac.uk 

