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:
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.
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:
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:
Short Introduction to R.
The main reference for the module is the following book: