MATH5835M — Statistical Computing

Contents

Syllabus

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:

Lecture Notes

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:

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 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

Handouts

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

Software

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:

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

Resources

Useful resources for learning R include to following:

R Code from Lectures (live and recorded)

References

The main reference for the module is the following book:

More in-depth information, beyond what we will be able to cover in the lectures, is for example contained in the following texts.

Links