Advanced Simulation Methods
Prof. Patrick Rebeschini, University of Oxford, Hilary term 2018
Course offered to Part C students (SC5) and MSc students (SM12)
Revisions (Trinity Term)
Revision Class 1 | Wednesday Week 2, 9.00am-10.30am, LG.01. We will cover the solutions of the 2016 Exams (Part C and MSc). |
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Revision Class 2 | Wednesday Week 4, 9.00am-11.00am, LG.01. We will cover the solutions of the 2017 Exams (Part C and MSc). |
Consultation Session (Part C students only) |
Wednesday Week 5, 9.00am-10.00am, LG.03. Only questions on the course material and the course problem sheets will be taken. Let the course instructor know which questions you would like to ask by completing this anonymous form click here |
General Information
Course Team | Patrick Rebeschini, Sebastian Schmon, Paul Vanetti |
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patrick.rebeschini AT stats.ox.ac.uk | |
Lectures | Mondays 9:00-10:00 & Wednesdays 9:00-10:00, weeks 1-8, LG.01 |
Tutorials | Weeks 3, 5, 6, 8 (details below) |
Tutorials
Group | Time | Location | Class Tutor / Teaching Assistant |
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Undergraduate 1 | Tuesdays 9:00-10:30, weeks 3, 5, 6, 8 | LG.04 | Patrick Rebeschini / Sebastian Schmon |
Undergraduate 2 | Tuesdays 10:30-12:00, weeks 3, 5, 6, 8 | LG.04 | Sebastian Schmon / Paul Vanetti |
MSc | Tuesdays 11:00-12:00, weeks 3, 5, 6, 8 | LG.02 | Patrick Rebeschini |
Syllabus
The aim of the lectures is to introduce modern simulation methods. This course concentrates on Markov chain Monte Carlo (MCMC) methods and Sequential Monte Carlo (SMC) methods. Examples of applications of these methods to complex inference problems will be given.- Classical Methods
- Inversion
- Rejection
- Composition
- Importance sampling
- MCMC Methods
- Elements of discrete-time general state-space Markov chains theory
- Metropolis-Hastings algorithm
- Gibbs sampling
- Slice sampling
- Tempering/annealing
- Reversible jump MCMC
- Pseudo-marginal MCMC
- Sequential importance sampling
- SMC methods
- Sequential Monte Carlo
- Nonlinear filtering
- C.P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd edition, Springer-Verlag, 2004
- J.S. Liu, Monte Carlo Strategies in Scientific Computing, Springer-Verlag, 2001
- B. D. Ripley, Pattern Recognition and Neural Networks, CUP, 1996
Notes
Here you can find the material accompanying the lectures.1 | Introduction | Notes » |
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2 | Inversion, Transformation and Rejection Sampling | Notes » |
3 | Importance Sampling and Variance Reduction | Notes » |
4 | Elements of Markov Chains Theory | Notes » |
5 | Gibbs Sampling | Notes » |
6 | Metropolis-Hastings | Notes » |
7 | Reversible Jump MCMC | Notes » |
8 | HMM and Sequential Importance Sampling | Notes » |
9 | Sequential Monte Carlo methods | Notes » |
Problem Sheets
These exercises will be covered in the tutorials. Solutions will be posted.Week 3 | due January 26th | Sheet » |
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Week 5 | due February 9th | Sheet » |
Week 6 | due February 16th | Sheet » |
Week 8 | due March 2nd | Sheet » |
Class allocation details are on Minerva (accessible from Oxford network).
Slides
Here you can find the slides accompanying the lectures.1 | Introduction | Slides » |
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2 | Introduction | Slides » |
3 | Inversion, transformation, composition, rejection | Slides » |
4 | Importance sampling | Slides » |
5 | Elements of Markov Chain theory | Slides » |
6 | Gibbs sampling | Slides » |
7 | Metropolis-Hastings | Slides » |
8 | Metropolis-Hastings | Slides » |
9 | Convergence diagnostic, tempering/annealing | Slides » |
10 | Reversible Jump | Slides » |
11 | Model selection, slice sampling | Slides » |
12 | Hidden Markov Models. Seq. Imp. Sampling (SIS) | Slides » |
13 | Sequential Importance Resampling (SIR) | Slides » |
14 | SIS and SIR: selected results | Slides » |
15 | Pseudo-marginal MCMC and parameters estimation | Slides » |
16 | Static problems | Slides » |
Feedback
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