NSCPHD1299 Markov chain Monte Carlo (MCMC)
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.
- Project work
- 5 ECTS
- Type of assessment
- Other, 3 days under invigilationWritten examination, One week under invigilationGroup 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.
- All aids allowed
- Marking scale
- passed/not passed
- Censorship form
- No external censorship