Comments on: Feedback on data cloning

By: ABC-MCMC for parallel tempering « Xi'an's Og

ABC-MCMC for parallel tempering « Xi'an's Og — Wed, 08 Feb 2012 23:13:03 +0000

[...] the algorithm. My first idea of a tempering mechanism in a likelihood-free setting was to replicate our SAME algorithm (Doucet, Godsill, and Robert, 2004), by creating Tj copies of the [pseudo-]observations to mimic [...]

By: xi'an

xi'an — Wed, 20 Jul 2011 07:13:19 +0000

Umberto: thanks for the comments and the thanks!
My feelings about the validation of a slowly varying k are that (a) you can correct for changing the power along the iterations, this is for instance what Radford Neal did in his tempered (1996) and annealed (2001) papers and (b) the method does not aim at correctly simulate from the powered distribution(s), rather at reaching the proper collection of global maxima. Hence incorrectly simulating from the powered target does not matter much in the end.

By: Umberto

Umberto — Tue, 19 Jul 2011 14:05:39 +0000

Dear Prof. Robert,

it is indeed surprising not to let k free to vary through the mcmc simulations as this is what we would expect to do in a simulated annealing procedure. However… I have a doubt regarding such approach (i.e. update k dynamically). If k is let free to grow, say linearly, through the mcmc algorithm, then the “likelihood” for cloned-data at the denominator of the acceptance probability in Lele et al. would be based on k clones whereas the likelihood corresponding to the proposal on the numerator would be computed using say k+1 cloned-data (or more). Wouldn’t this represent an unfair comparison between proposal and last chain value? This way the likelihhod for the proposal would be based on a larger amount of “data”.
I would appreciate your thought on this.

Thank you very much for running such an interesting blog (and for your books of course!).