#### 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). Wednesday Week 4, 9.00am-11.00am, LG.01.We will cover the solutions of the 2017 Exams (Part C and MSc). 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
Previous exams can be found in WebLearn. For Part C exams, look for the "Advanced Simulation Methods" papers (three questions per paper). For MSc exams, look for the "Further Statistical Methodology" papers. MSc papers list questions from multiple courses, including Advanced Simulation Methods (two questions per paper).

## General Information

Course Team Patrick Rebeschini, Sebastian Schmon, Paul Vanetti patrick.rebeschini AT stats.ox.ac.uk Mondays 9:00-10:00 & Wednesdays 9:00-10:00, weeks 1-8, LG.01 Weeks 3, 5, 6, 8 (details below)

## Tutorials

Group Time Location Class Tutor / Teaching Assistant
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 2 Introduction Notes » Inversion, Transformation and Rejection Sampling Notes » Importance Sampling and Variance Reduction Notes » Elements of Markov Chains Theory Notes » Gibbs Sampling Notes » Metropolis-Hastings Notes » Reversible Jump MCMC Notes » HMM and Sequential Importance Sampling Notes » Sequential Monte Carlo methods Notes »

## Problem Sheets

These exercises will be covered in the tutorials. Solutions will be posted.

Week 3 Week 5 Week 6 due January 26th Sheet » Solutions » 1.1 1.2 1.3 1.4 1.5 due February 9th Sheet » Solutions » 2.1 due February 16th Sheet » Solutions » 3.1 due March 2nd Sheet » Solutions » 4.1 4.2 4.3
For undergraduate students: hand in solutions by Friday 13:00 before class at the Advanced Simulation tray.

Class allocation details are on Minerva (accessible from Oxford network).

## Slides

Here you can find the slides accompanying the lectures.

1 2 Introduction Slides » Introduction Slides » Inversion, transformation, composition, rejection Slides » Importance sampling Slides » Elements of Markov Chain theory Slides » Gibbs sampling Slides » Metropolis-Hastings Slides » Metropolis-Hastings Slides » Convergence diagnostic, tempering/annealing Slides » Reversible Jump Slides » Model selection, slice sampling Slides » Hidden Markov Models. Seq. Imp. Sampling (SIS) Slides » Sequential Importance Resampling (SIR) Slides » SIS and SIR: selected results Slides » Pseudo-marginal MCMC and parameters estimation Slides » Static problems Slides »

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