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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:
The lecture videos which I recorded during the Covid 19 pandemic can be found by clicking on the video number in the following table, or all together in the MATH5835M video playlist.
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:
| videos | sections | pages | topic |
|---|---|---|---|
| 1, 2, 3, 4 | 3.1 | 69-74 | Monte Carlo methods |
| 5, 6, 7 | 3.2 | 75-84 | 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,
39,
40, 41, 42, 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. I will publish more information about the practical later in the semester.
The following links contain problem sheets for self-study.
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:
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