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 An Introduction
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 lectures.

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 homepage.
- A more polished version is RStudio, which can be found at
the RStudio homepage. (Choose
the open source version,
RStudio Desktop

, on the download page.)

Alternatively you can use RStudio or plain R on the university computers.

Useful resources for learning R include to following:

- The stats department provides a short, four-page 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
my
Short Introduction to R

. - The official R manual contains a lot of information.
- The R online help, accessed by typing help() 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).

- homework1.R
- ImportanceSampling.R
- antithetic.R
- ControlVariates.R
- LCG.R
- InverseTransform.R
- lecture-Oct19.R
- Pareto-Nov2.R
- basicRejection1.R
- basicRejection2.R
- NormalViaRejection.R
- envelope-Nov5.R
- IS-Nov9.R
- simpleMC.R
- MCMC-Poiss.R
- RWM.R
- MCMC-Nov23.R
- MCMC-Covid.R
- bootstrap-bias.R
- bootstrap-se.R

The main reference for the module is the following book:

- Jochen Voss,
*An Introduction to Statistical Computing: A Simulation-Based Approach*.

Wiley, 2014 (Library, Amazon)

- Maria L. Rizzo,

*Statistical Computing with R*.

Chapman & Hall/CRC, 2008 (Library, Amazon) - Brian D. Ripley,

*Stochastic Simulation*.

Wiley, 1987 (Library, Amazon) - Christian P. Robert and George Casella,

*Monte Carlo Statistical Methods*.

Springer, 2004 (Library, Amazon) - Wally R. Gilks, Silvia Richardson and David J. Spiegelhalter,

*Markov Chain Monte Carlo in Practice*.

Chapman & Hall/CRC, 1995 (Library, Amazon) - Anthony C. Davison and David V. Hinkley,

*Bootstrap methods and their application*.

Cambridge University Press, 1997 (Library, Amazon) - Andrew Gelman,
*et al.*,

*Bayesian Data Analysis*.

Chapman & Hall/CRC, 3rd edition, 2013 (Library, Amazon)

- MATH5835M module catalog entry
- The university timetable/room plan