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NSCPHD1299  Markov chain Monte Carlo (MCMC) Volume 2013/2014

Course information

LanguageEnglish
Credit5 ECTS
LevelPh.D.
Duration
The course begins on the morning of Tuesday September 17th 2013 and closes at lunchtime on Friday September 20th 2013.
Placement
Autumn
Schedule
The course begins on the morning of Tuesday September 17th 2013 and closes at lunchtime on Friday September 20th 2013.
Course capacityIt is recommended to sign up as soon as possible due to a restricted number of participants. Note that the registration is NOT completed until you recieve a confirmation email
Continuing and further education
Study boardNatural Sciences PhD Committee
Contracting department
  • Department of Mathematical Sciences
Course responsible
  • Susanne Ditlevsen (7-7a7c7a6875756c4774687b6f35727c356b72)
Teachers
•Omiros Papaspiliopoulos (Universitat Pompeu Fabra, Barcelona)
•Gareth O. Roberts (Warwick University)
Saved on the 24-09-2013
Content

The course is about Markov chain Monte Carlo (MCMC) algorithms. We motivate the need for such algorithms with some canonical problems from Statistics and Stochastic Processes. We describe various popular algorithms and discuss the main tool to produce new algorithms (invariance). We carry out simple experiments that point out the strengths and limitations of MCMC algorithms and then embark on the investigation of their theoretical properties with the aim at redesigning them, precisely when they perform poorly. To this end, in parallel we review the fundamental (Meyn & Tweedie) theory of Markov chains on general state spaces (irreducibility, regeneration, recurrence, notions of ergodicity) and elaborate it for Markov chains generated by MCMC algorithms. We then outline some generic strategies for redesigning algorithms (reparameterisations & scaling) together with the associated theory. We close the course with a presentation of recent methods that have enriched significantly the MCMC toolbox and are particularly relevant when faced with very high (or infinite) dimensional statistical models and/or intractable likelihoods (retrospective sampling, MCMC on Hilbert spaces, pseudo-marginal algorithms). The material is largely based on a forthcoming book by Papaspiliopoulos, Roberts and Tweedie.

 

Teaching and learning methods
A combination of lectures and exercises for four intensive days.
Academic qualifications
Phd student in statistics or similar. Some familiarity with programming in R or similar is recommended.
Sign up
Exam
Credit5 ECTS
Type of assessment
Other, 3 days under invigilation
Written examination, One week under invigilation
Group project: 60%

The course will contain a mandatory group project and each participant will be assigned to one project which is to be done during the course. The topics are: Mixture models for clustering, State-space models in time series, Bayesian variable selection in regression, Stochastic epidemic models. The students will be arranged in groups of 4-5 people. The projects will be open ended - no correct answer will exist! The aim is to experiment creatively and learn the challenges and inner workings of MCMC under supervision. The students will present their work and results (blackboard/projector but no typed text expected) on Thursday, from 17.00-18.30. The assessment will not be strict, the point is to get the students trying things out as a research project.

Individual assessment: 40%

Solve 6 theoretical exercises related to the course contents, to be sent by email one week after the end of the course.
AidAll aids allowed
Marking scalepassed/not passed
Censorship formNo external censorship
Workload
CategoryHours
Lectures20
Project work10
Laboratory4
Exam50
Preparation48
Excursions5
Total137
Saved on the 24-09-2013