parallel Metropolis Hastings [published]

As I was looking at the discussion paper by Yamin Yu and Xiao-Li Meng on improved efficiency for MCMC algorithms, which is available (for free) on-line, I realised the paper on parallel Metropolis-Hastings algorithm we wrote with Pierre Jacob and Murray Smith is now published in Journal of Computational and Graphical Statistics (on-line). This is a special issue for the 20th anniversary of the Journal of Computational and Graphical Statistics and our paper is within the “If Monte Carlo Be a Food of Computing, Simulate on” section! (My friends Olivier Cappé and Radu V. Craiu also have a paper in this issue.)  Here is the complete reference:

P. Jacob, C. P. Robert, & M. H. Smith. Using Parallel Computation to Improve Independent Metropolis–Hastings Based Estimation. Journal of Computational and Graphical Statistics. September 1, 2011, 20(3): 616-635. doi:10.1198/jcgs.2011.10167

The [20th Anniversary Featured Discussion] paper by Yamin Yu and Xiao-Li Meng has already been mentioned on Andrew’s blog, it is full of interesting ideas and remarks about improving Gibbs efficiency, in the spirit of the very fine work Jim Hobert and his collaborators have been developing in the past decade,  fun titles (“To center or not center – that is not the question”, “coupling is more promising than compromising”, “be all our insomnia remembered”, and “needing inception”, in connection with the talk Xiao-Li gave in Paris two months ago….), and above all the fascinating puzzle of linking statistical concepts and Monte Carlo concepts. How comes sufficiency and ancillarity are to play a role in simulation?! Where is the simulation equivalent of Basu’s theorem? These questions obviously relate to the idea of turning simulation into a measure estimation issue, discussed in a post of mine after the Columbia workshop. This interweaving paper also brings back memories of the fantastic Biometrika 1994 interleaving paper by Liu, Wong, and Kong, with its elegant proof of positive decreasing correlation and of improvement by Rao-Blackwellisation [another statistics theorem!] for data augmentation.