On the Use of Backward Simulation in the Particle Gibbs Sampler
2012 (English)In: Proceedings of the 37th IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE , 2012, 3845-3848 p.Conference paper (Refereed)
The particle Gibbs (PG) sampler was introduced in [Andrieu et al. (2010)] as a way to incorporate a particle filter (PF) in a Markov chain Monte Carlo (MCMC) sampler. The resulting method was shown to be an efficient tool for joint Bayesian parameter and state inference in nonlinear, non-Gaussian state-space models. However, the mixing of the PG kernel can be very poor when there is severe degeneracy in the PF. Hence, the success of the PG sampler heavily relies on the, often unrealistic, assumption that we can implement a PF without suffering from any considerate degeneracy. However, as pointed out by Whiteley in the discussion following [Andrieu et al. (2010)], the mixing can be improved by adding a backward simulation step to the PG sampler. Here, we investigate this further, derive an explicit PG sampler with backward simulation (denoted PG-BSi) and show that this indeed is a valid MCMC method. Furthermore, we show in a numerical example that backward simulation can lead to a considerable increase in performance over the standard PG sampler.
Place, publisher, year, edition, pages
IEEE , 2012. 3845-3848 p.
, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ISSN 1520-6149
Gibbs sampling, Particle Markov chain Monte Carlo, Backward simulation, Particle Gibbs, Particle filterm, Gibbs sampling
IdentifiersURN: urn:nbn:se:liu:diva-81262DOI: 10.1109/ICASSP.2012.6288756ISI: 000312381403228ISBN: 978-1-4673-0044-5ISBN: 978-1-4673-0045-2OAI: oai:DiVA.org:liu-81262DiVA: diva2:551257
37th IEEE International Conference on Acoustics, Speech, and Signal Processing, Kyoto, Japan, 25-30 March, 2012
FunderSwedish Research Council