MATH30034 - 2006/2007

 

Specification

Aims

To teach statistical modelling and inferences at the third year level.

Brief Description of the unit

This course teaches statistical modelling and inferences at the third year level. It begins with maximum likelihood, and the rest of the module follow this theme. The statistical package S-PLUS is used whenever appropriate.

Learning Outcomes

On successful completion of the course students will

• be able to fit certain distributions or models by maximum likelihood;
• be able to check model adequacy and make inferences;
• have experience of writing statistical reports.

Future topics requiring this course unit

MATH40361 Computationally Intensive Statistics

Syllabus

1. Introduction to (or revision of) S-PLUS [2]
2. Maximum likelihood estimation: likelihood and log-likelihood functions, normal equations, Newton-Raphson algorithm, Fisher's information and asymptotic normality (no proof), deviance, Likelihood-ratio tests. Project 1. [4]
3. Nonlinear regression: model specification, least squares estimation, Gauss-Newton algorithm and its modifications, residual analysis, inferences. Project 2. [4]
4. ARMA models: model specification, causality and invertibility conditions, estimation of parameters by maximum likelihood, choosing model by AIC/BIC, prediction. Project 3. [4]
5. Gaussian mixture Models and the EM algorithm: model specification, complete/incomplete data likelihoods, the E-step and the M-step, implementation. Project 4. [4]
6. Kernel density estimation and classification: the histogram, kernel smoothing, choice of bandwidth, classification problem, maximum likelihood rule. Project 5. [4]

Textbooks

W. N. Venables and B. D. Ripley, Modern Applied Statistics with S, Springer-Verlag (4th edition, 2002),

D. M. Bates and D. G. Watt, Nonlinear Regression Analysis and Its Applications, Wiley (1988),

P. J. Brockwell and R. A. Davis, Time Series: Theory and Practice, Springer-Verlag (1996),

G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, Wiley-Interscience (1966),

B. W. Silverman, Density Estimation for Statistical Data Analysis, Chapman and Hall, London (1986).

Teaching and learning methods

Two lectures per week plus one weekly computer class.

Assessment

100% coursework (choice of four projects from five offered).

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