Unit information: Statistical Computing in 2017/18

Unit name	Statistical Computing
Unit code	MATHM6007
Credit points	10
Level of study	M/7
Teaching block(s)	Academic Year (weeks 1 - 52)
Unit director	Dr. Kovac
Open unit status	Not open
Pre-requisites	None
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

This unit provides a practical introduction to the fundamentals of numerical computation for students of statistics. It will cover basic numerical linear algebra, optimization methods, numerical differentiation and integration and techniques for random number generation. The general prerequisites are a working knowledge of the statistical package R (and preferably some knowledge of a lower level language such as C, Pascal or even Fortran), together with a basic familiarity with standard undergraduate results in linear algebra and calculus. By the end of the units, students should be able to write stable, fast and numerically accurate statistical code. The topics covered may include: Numerical linear algebra (with applications): basic efficiency, Choleski, QR, stability, eigen and singular value decompositions, public LA libraries. Optimization: Newton type methods, Gauss-Newton, stochastic optimization. Differentiation by computer: finite differencing (proper interval choice), automatic differentiation. Numerical Integration: quadrature, ODE methods, stochastic. The basics of random number generation.

Aims:

The aim of this unit is to introduce, in a practical way, the fundamentals of numerical computation for statistics, to enable students to write stable, fast and numerically accurate statistical code.

Only available as part of a 1+ 3 Statistics MRes + PhD programme.

Intended Learning Outcomes

• To understand the importance of stability, efficiency and accuracy in numerical computations, and how these may be promoted in practical statistical computation.

• To understand the main issues that arise in the topics given above, and to be aware of standard libraries and other resources for numerical computation.

• To be able to write code, including library routines where appropriate, to perform simple standard tasks in each of the areas covered by the topics.

Teaching Information

Lectures and statistical computing laboratory work, supported by seminars and tutorials.

Assessment Information

Assessment with be based on an extended assignment, bringing together several of the topics covered. For example writing a routine to estimate a linear mixed model by (RE)ML.

The assessment criteria for the assignment will be based on a suitably modified version of the current Mathematics Department Project Assessment form. The assignment will be marked by the member of staff in charge of the unit and by an independent second marker.

Reading and References

• Gill, P.E., Murray, W. and Wright, M.H., Practical Optimization, Academic Press, 1981

• Lange, K., Numerical Analysis for Statisticians, Springer, 2000

• Watkins, D.S., Fundamentals of Matrix Computation, Wiley, 1991

• Wood, S. N., Generalized Additive Models – An Introduction with R, Chapman & Hall, 2006