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
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 exact page ranges are:
to Statistical Computing: A Simulation-Based Approach
(see References, below), which was specially
written for this module. The book is available online
via the university library:
|1, 2, 3, 4
||Monte Carlo methods
|5, 6, 7
||Monte Carlo error
|10, 11, 12
||Antithetic Variables method
||Control Variates method
|15, 16, 17
||Pseudo Random Number Generators
||Inverse Transform method
|20, 21, 22
||basic rejection sampling
|23, 24, 25
||envelope rejection sampling
|26, 27, 28
|29, 30, 31
||Metropolis-Hastings (MH) algorithm
|32, 33, 34
||special cases of the MH algorithm
|35, 36, 37
||Convergence of MCMC estimates
|38 -- 43
||(intro of 4.3)
||Application to Bayesian Inference
|44, 45, 46
||Applications to statistical inference
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.
R Code from Lectures (live and recorded)
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