PhD Course on MCMC in Statistics
Tuesday September 17th - Friday September 20th, 2013
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.
- Omiros Papaspiliopoulos (Universitat Pompeu Fabra, Barcelona)
- Gareth O. Roberts (Warwick University)
The course begins on the morning of Tuesday September 17th 2013 and closes at lunchtime on Friday September 20th 2013. A detailed schedule will be available here .
The work load of the course corresponds to 5 ECTS.
The course is primarily aimed at PhD students from Science but is open to others as well on a first-come, first-served basis. A list of participants will be available here .
There will be a social dinner on Thursday September 19th.
Unfortunately we do not have the possibility to give financial support.
- Anders Jensen (Contact person)
- Susanne Ditlevsen
- Omiros Papaspiliopoulos
- Gareth O. Roberts