Uniform Ergodicity of the Particle Gibbs Sampler
2015 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 42, no 3, 775-797 p.Article in journal (Refereed) Published
The particle Gibbs sampler is a systematic way of using a particle filter within Markov chain Monte Carlo. This results in an off-the-shelf Markov kernel on the space of state trajectories, which can be used to simulate from the full joint smoothing distribution for a state space model in a Markov chain Monte Carlo scheme. We show that the particle Gibbs Markov kernel is uniformly ergodic under rather general assumptions, which we will carefully review and discuss. In particular, we provide an explicit rate of convergence, which reveals that (i) for fixed number of data points, the convergence rate can be made arbitrarily good by increasing the number of particles and (ii) under general mixing assumptions, the convergence rate can be kept constant by increasing the number of particles superlinearly with the number of observations. We illustrate the applicability of our result by studying in detail a common stochastic volatility model with a non-compact state space.
Place, publisher, year, edition, pages
Wiley , 2015. Vol. 42, no 3, 775-797 p.
conditional sequential Monte Carlo; particle Gibbs; particle Markov chain Monte Carlo; particle smoothing; state space models
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:liu:diva-121304DOI: 10.1111/sjos.12136ISI: 000360077100009OAI: oai:DiVA.org:liu-121304DiVA: diva2:854299
Funding Agencies|project Learning of complex dynamical systems - Swedish Research Council [637-2014-466]2015-09-162015-09-142015-11-05