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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Likelihood and Generalized Linear Models (MATH11121)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits10 ECTS Credits5
SummaryThe concept of likelihood is central to statistical inference. This course develops likelihood methods for single parameter and multiparameter problems, including iterative maximum likelihood estimation, likelihood-based 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Foundations of Calculus (MATH08005) AND Several Variable Calculus (MATH08006) AND Linear Algebra (MATH08007) AND Methods of Applied Mathematics (MATH08035) AND Probability (Year 2) (MATH08008) AND Statistics (Year 2) (MATH08051))
Co-requisites
Prohibited Combinations Other requirements None
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
KeywordsLGLM
Contacts
Course organiserDr Bruce Worton
Tel: (0131 6)50 4884
Email: Bruce.Worton@ed.ac.uk
Course secretaryMrs Frances Reid
Tel: (0131 6)50 4883
Email: f.c.reid@ed.ac.uk
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