# Computational Statistics

## Module description

The course is designed to introduce you to the modern computational methods of statistics, which have had an enormous impact on statistical practice over the past 30 years. These methods, sometimes called Monte Carlo methods, are computationally intensive techniques and the breadth of such methods and their application is extensive.

The course aims to give you an understanding and appreciation of many of the ideas underlying these methods. It aims to review a range of techniques, illustrate how they may be applied in practice and give you computational experience in applying them using a high-level programming language such as R.

### Indicative module syllabus

• The uses and aims of simulation in statistical inference
• Pseudo-random numbers
• Generation of random variables: principles, techniques and examples
• Inversion and rejection methods for obtaining random samples from arbitrary distributions (given uniformrandom samples)
• Application to include binomial, Poisson, gamma and normal distributions
• Variance reduction methods
• Randomisation tests
• The bootstrap and the jackknife: bootstrap for estimation, bootstrap confidence sets and hypothesis tests
• The EM algorithm and its uses: examples of applications, implementational issues
• An introduction to non-parametric regression, smoothing and kernel density estimation

## Learning objectives

By the end of this module, you should be able to demonstrate:

• knowledge and understanding of the theory, techniques and computational methods for simulation in the context of statistical inference
• knowledge and understanding of the theory and application of re-sampling techniques such as the bootstrap
• knowledge and understanding of the theory and practical issues involved in modern non-parametric modelling
• the ability to make sensible use of a range of modern computationally intensive techniques and algorithms to model and draw inferences from statistical data
• the ability to program and use advanced mathematical and statistical software to carry out computationally intensive statistical methods
• the ability to incorporate the results of a technical analysis into clearly written report form that may be understood by a non-specialist.