# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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# Postgraduate Course: Likelihood and Generalized Linear Models (MATH11121)

 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, 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.
 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
 Not being delivered
 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.
 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.
 Graduate Attributes and Skills Not entered Keywords LGLM
 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
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