Simulation and Statistical Programming Hilary Term 2020

General information

Lecturer: Robert Davies (email robertwilliamdavies@gmail.com)
Class tutors / TAs: Anthony Caterini (email anthony.caterini@stats.ox.ac.uk), Bobby He (email bobby.he@spc.ox.ac.uk), Sheheryar Zaidi (email sheheryar.zaidi@some.ox.ac.uk)
Demonstrators: Alan (Siu Chau) (email siu.chau@spc.ox.ac.uk)

Synopsis

Simulation: Transformation methods. Rejection sampling including proof for a scalar random variable, Importance Sampling. Unbiased and consistent IS estimators. MCMC including the Metropolis-Hastings algorithm.
Statistical Programming: Numbers, strings, vectors, matrices, data frames and lists, and Boolean variables in R. Calling functions. Input and Output. Writing functions and flow control. Scope. Recursion. Runtime as a function of input size. Solving systems of linear equations, Cholesky decomposition. Numerical stability. Regression and least squares, QR factorisation. Implementation of Monte Carlo methods for elementary Bayesian inference.
See full sypnosis on departmental website here and handbook supplement pdf here.

Timetable

Week	Lecture Tuesday 2-3pm LG.02, the IT suite, 24-29 Saint-Giles'	Computer Lab Friday 9-11am LG.02, the IT suite, 24-29 Saint-Giles'	Problem class Various times 24-29 Saint-Giles'
1	X
2	X
3	X	X	X
4	X	X
5	X	X	X
6	X	X
7	X	X	X
8	X	X
TT1			X

Problem class details and sheets

Class	Tutor	TA	Time	Location weeks HT3, 5, 7	Location week TT1
1	Robbie Davies	Sheheryar Zaidi	Wednesday 9AM	LG.02	LG.02
2	Anthony Caterini	Anthony Caterini	Thursday 11-12PM	LG.02	LG.03
3	Anthony Caterini	Sheheryar Zaidi	Thursday 10-11AM	LG.02	LG.03
4	Bobby He	Bobby He	Wedesnday 4-5PM	LG.04	LG.04

Please hand in the solutions to the problem sheets by Monday noon of weeks 3, 5, 7 and send the R code by email, in a single well-commented R-script to the class TA.

Simulation lectures

Lecture slides with previous year contents and format are available here, here, and here. I will be minimally modifying these slides for this year. I will post the slides I will use below a few days before class.

Lecture 1, Introduction and Monte Carlo method.
Lecture 2, Inversion & transformation methods
Lecture 3, Rejection sampling
Lecture 4, Importance sampling
Lecture 5, Normalized importance sampling
Lecture 6, Markov chain Monte Carlo
Lecture 7, Markov chain Monte Carlo: Metropolis-Hastings
Lecture 8, Markov chain Monte Carlo: Gibbs sampling

Statistical programming lectures, problem sheets and solutions

Week	Slides	Practical	Solutions	Code	Extra
3	Slides 1	Practical 1	Solutions 1
4	Slides 2	Practical 2	Solutions 2	Code 2
5	Slides 3	Practical 3	Solutions 3	Code 3
6	Slides 4	Practical 4	Solutions 4	Code 4
7	Slides 5	Practical 5	Solutions 5	Code 5
8	Slides 6	Practical 6	Solutions 6	Code 6	MHcode.R

Handouts (fewer pages, same information) of the slides are available here, as well as 4 per page here.

Datasets: Cystic Fibrosis (cystfibr.txt), Tetrahymena Data (hellung.txt), Japanese beetle larvae data (beetlelarva.txt), Speed Data (speed.txt), Air Pollution Data (airpol.txt), Image Data (image_noisy.txt, image_true.txt).

Past course material

Julien Berestycki Simulation 2019.
Geoff Nicholls Statistical Programming 2019.
Geoff Nicholls Statistical Programming 2015.
Geoff Nicholls Simulation Notes (very useful).

Resources

We will be using the statistical software package R, which you can get here. Please install it on your own computer and practice using it as early as possible. You may find it helpful to bring a laptop to use during lectures, but it is not necessary.

The software RStudio is also useful.

You may find it useful to use R through a text editor. If you can stomach the learning curve of memorizing a few dozen key combinations, I highly recommend Emacs Speaks Statistics. You can download an all in one installer if you use a mac laptop here. The benefit of ESS is that the development environment when you use a laptop or a server is the same. This facilitates development in the real world, where almost always, the data is too sensitive to download locally, or your local workstation / laptop has insufficient storage or power to perform analysis locally.

Credit

This course material was almost entirely prepared by others who lectured this course earlier, including at least Julien Berestycki, Geoff Nicholls and Robin Evans.