J. R. Statist. Soc. B (2010) 72, Part 3, pp. 269–342 Particle Markov chain Monte Carlo methods Christophe Andrieu, University of Bristol, UK Arnaud Doucet University of British Columbia, Vancouver, Canada, and Institute of Statistical Mathematics, Tokyo, Japan and Roman Holenstein University of British Columbia, Vancouver, Canada [Read before The Royal Statistical Society at a meeting organize