MATH48091 - 2010/2011

 

Specification

Aims

To introduce the student to computational statistics, both the underlying theory and the practical applications.

Brief Description of the unit

Computers are an invaluable tool to modern statisticians. The increasing power of computers has greatly increased the scope of inferential methods and the type of models which can be analysed. This has led to the development of a number of computationally intensive statistical methods, many of which will be introduced in this course.

Learning Outcomes

On successful completion of this course unit students will be able to

• appreciate the usefulness of computational methods in modern statistics;
• understand the basic ideas underpinning the theory;
• be able to apply the methodology to standard problems.

Future topics requiring this course unit

MATH48122 Computationally Intensive Statistics

Syllabus

Items 1 -5 are taught by Dr Peter Neal, while item 6 is taught by Dr Jingsong Yuan.

1. Simulating random variables: inversion, rejection, ratio of uniforms, transformations. [4]
2. Monte Carlo integration: introduction, importance sampling, antithetic variables, control variates. [4]
3. Kernel density estimation. [2]
4. Non-parametric Bootstrap and Jackknife. [3]
5. Nonlinear regression: model specification, least squares estimation, Gauss-Newton algorithm. [3]
6. EM algorithm: Data augmentation, mixture distributions, censored data, standard errors, Monte-Carlo EM. [6]

Textbooks

Rizzo, M. L., Statistical Computing with R. Chapman & Hall.

Teaching and learning methods

Two lectures + two hour computer workshop each week. In addition students should expect to spend at least 6 hours each week on private study for this course unit.

Assessment

ten pieces of coursework : 50%

End of semester written examination (2 hours): 50%

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Arrangements