running MCMC for too long, and even longer…

Clifton observatory, Clifton, Sept. 24, 2012Following my earlier post about the young astronomer who feared he was running his MCMC for too long, here is an update from his visit to my office this morning.  This visit proved quite an instructive visit for both of us. (Disclaimer: the picture of an observatory seen from across Brunel’s suspension bridge in Bristol is as earlier completely unrelated with the young astronomer!)

First, the reason why he thought MCMC was running too long was that the acceptance rate was plummeting down to zero, whatever the random walk scale. The reason for this behaviour is that he was actually running a standard simulated annealing algorithm, hence observing the stabilisation of the Markov chain in one of the (global) modes of the target function. In that sense, he was right that the MCMC was run for “too long”, as there was nothing to expect once the mode had been reached and the temperature turned down to zero. So the algorithm was working correctly.

Second, the astronomy problem he considers had a rather complex likelihood, for which he substituted a distance between the (discretised) observed data and (discretised) simulated data, simulated conditional on the current parameter value. Now…does this ring a bell? If not, here is a three letter clue: ABC… Indeed, the trick he had found to get around this likelihood calculation issue was to re-invent a version of ABC-MCMC! Except that the distance was re-introduced into a regular MCMC scheme as a substitute to the log-likelihood. And compared with the distance at the previous MCMC iteration. This is quite clever, even though this substitution suffers from a normalisation issue (that I already mentioned in the post about Holmes’ and Walker’s idea to turn loss functions into pseudo likelihoods. Regular ABC does not encounter this difficult, obviously. I am still bemused by this reinvention of ABC from scratch!  

So we are now at a stage where my young friend will experiment with (hopefully) correct ABC steps, trying to derive the tolerance value from warmup simulations and use some of the accelerating tricks suggested by Umberto Picchini and Julie Forman to avoid simulating the characteristics of millions of stars for nothing. And we agreed to meet soon for an update. Indeed, a fairly profitable morning for both of us!

3 Responses to “running MCMC for too long, and even longer…”

  1. I think the reinventions of these algorithms must be pretty common. Coming to the Bayesian estimation literature from a computational/biology background I have often had the conversation with colleagues in statistics where I’m speculating about some idea on how to resolve a computational problem and they say “oh yeah, I think that’s called X. Here’s a reference for how to implement it.” It saves a lot of time once you learn the names—I don’t want to “reinvent” statistics.

  2. Cool. I’ve been trying to popularize ABC in astronomy (via my 2012 MNRAS paper), but it’s not yet come to many people’s awareness. Two other interesting reinventions of ABC in astronomy are by Kashyap & co (“Flare Heating in Stellar Coronae”) in 2002 and Vaughan et al. (“On characterising the variability properties of X-ray light curves from active galaxies”) in 2003!

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