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Non-reversible operators for MCMC

January 15, 2015

Been visiting University of Helsinki since Christmas and there is Jukka Corander, a Bayesian statistician who works on variants of MCMC and pseudo-likelihood, ways of scaling up statistical computation.  He showed me his 2006 Statistics and Computing paper on “Bayesian model learning based on a parallel MCMC strategy,” (PDF around if you search) and I have to say I’m amazed.  This is so important, as anyone who tries MCMC in complex spaces would know.  The reason for wanting these is:

  • proposal operators for things like split-merge must propose *reasonable* alternatives and therefore this must be done with a non-trivial operator
    • e.g.,  greedy search is used to build an initial split for the proposal
  • developing the reverse operator for these is very hard

So Jukka’s groups result is that reversible MCMC is not necessary.  As long as the usual Metropolis-Hastings acceptance condition applies, the MCMC process converges in the long term.

Anyway, I can now build split-merge operators using MCMC without requiring crazy reversability!

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