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. The book is available online
via the university library:

videos | sections | pages | topic |
---|---|---|---|

1, 2, 3, 4 | 3.1 | 69--74 | Monte Carlo methods |

5, 6, 7 | 3.2 | 74--84 | Monte Carlo error |

8, 9 | 3.3.1 | 84--88 | Importance Sampling |

10, 11, 12 | 3.3.2 | 88--93 | Antithetic Variables method |

13, 14 | 3.3.3 | 93--96 | Control Variates method |

15, 16, 17 | 1.1 | 1--8 | Pseudo Random Number Generators |

18, 19 | 1.3 | 11--15 | Inverse Transform method |

20, 21, 22 | 1.4.1 | 15--18 | basic rejection sampling |

23, 24, 25 | 1.4.2 | 18--22 | envelope rejection sampling |

26, 27, 28 | 2.3 | 50--58 | Markov Chains |

29, 30, 31 | 4.1.1--4.1.2 | 110--116 | Metropolis-Hastings (MH) algorithm |

32, 33, 34 | 4.1.3--4.1.4 | 116--120 | special cases of the MH algorithm |

35, 36, 37 | 4.2.2 | 129--137 | Convergence of MCMC estimates |

38 -- 43 | (intro of 4.3) | 137--139 | Application to Bayesian Inference |

44, 45, 46 | 5.2.1 | 192--197 | Bootstrap sampling |

47, 48 | 5.2.2.1, 5.2.2.2 | 198--203 | Applications to statistical inference |

The practical is an assessed part of the module. It counts 20%
towards the final grade. The deadline for submitting your solution
is **Friday, 19th November, 2pm**.

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

- homework sheet 1, answers
- homework sheet 2, answers
- homework sheet 3, answers
- homework sheet 4, answers
- homework sheet 5, answers

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 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