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

The following links contain pdf copies of the handouts from the lectures.

- general information
- practical, solutions as

html, pdf, RStudio notebook

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).

- lect-2018-10-01.R — A short program to estimate $\mathbb{E}(U^2)$ where $U \sim \mathcal{U}[0,1]$.
- lect-2018-10-11.R — Partial solutions for homework sheet 1.
- lect-2018-10-18.R — An example for the antithetic variables method.
- lect-2018-10-25.R — Partial solutions for homework sheet 2.
- lect-2018-11-01.R — Rejection sampling for the semi-circle distribution.
- lect-2018-11-22a.R and lect-2018-11-22b.R — Two experiments to illustrate the Metropolis-Hastings algorithm.
- lect-2018-12-06.R — Code for exercise 13.
- lect-2018-12-10.R — Illustration for the bootstrap estimte of the bias.

The module will be self-contained, *i.e.* you will not be
required to read/buy/borrow any books. In case you want to do further
reading, a good source is the following book, which was specially
written for the module:

- 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