MATH5835M — Statistical Computing
Statistical computing is the branch of computational
mathematics which studies computational techniques for situations
which either directly involve randomness, or where randomness is used
as part of a mathematical method. This module gives an introduction
to statistical computing, with a focus on Monte Carlo methods. The
following topics will be covered:
- Monte-Carlo methods
- Random number generation
- Markov Chain Monte Carlo (MCMC) methods
- Resampling methods
- Implementation of different methods in R
In place of lecture notes, we will use the book
to Statistical Computing: A Simulation-Based Approach
(see References, below), which was specially
written for this module. We will cover sections 3.1-3.3, 1.1, 1.3,
1.4, 2.3, 4.1, 4.2 and 5.2 of this book. The book is available online
via the university library:
The following links contain pdf copies of the handouts from the
For the module we will use the statistical computing package R.
This program is free software, and I would recommend that you install
R on your own laptop. There are different versions of R available:
- R itself, together with a lot of additional information, can be
found on the R project
- A more polished version is RStudio, which can be found at
the RStudio homepage. (Choose
the open source version,
RStudio Desktop, on the download
Alternatively you can use RStudio or plain R on the university
Useful resources for learning R include to following:
- The stats department provides a short,
introduction to R. This covers, amongst other things, how to
start R on the university's computers and has some hints on how to
install R on your own computer.
- The basics of R are explained in a bit more detail in
Short Introduction to
R manual contains a lot of information.
- The R online help, accessed by
or help.start() in R, can be used to
remind yourself about indivdual commands.
- An R tutorial can be found in appendix B of my book An
Introduction to Statistical Computing: A Simulation-Based Approach
(the first reference below).
R Code from Lectures
The main reference for the module is the following book:
More in-depth information, beyond what we will be able to cover in the
lectures, is for example contained in the following texts.
- Jochen Voss,
An Introduction to Statistical
Computing: A Simulation-Based Approach.
- Maria L. Rizzo,
Statistical Computing with R.
Chapman & Hall/CRC, 2008
- Brian D. Ripley,
Wiley, 1987 (Library,
- Christian P. Robert and George Casella,
Monte Carlo Statistical Methods.
- Wally R. Gilks, Silvia Richardson and David J. Spiegelhalter,
Markov Chain Monte Carlo in Practice.
Chapman & Hall/CRC, 1995
- Anthony C. Davison and David V. Hinkley,
Bootstrap methods and their application.
Cambridge University Press, 1997
- Andrew Gelman, et al.,
Bayesian Data Analysis.
Chapman & Hall/CRC, 3rd edition, 2013