Thank you for the update, Umberto, and for referring to our 1993, 1998 and 2002 papers as predating data cloning! And for accounting for my earlier comments.

]]>Comparisons with ABC-MCMC are also reported and we give some insight (see the final Summary section) on how to exploit our data-cloning ABC for when model simulations are expensive. The g-and-k example also show how the Beaumont’s regularization allows rapid increase in the clones number. Interestingly, when cloning is “cheap” (e.g. by using a carefully vectorized code) this translate in a reduced number of (ABC)MCMC iterations which are overall less expensive than a regular ABC-MCMC. ]]>

Yes of course when I say that “we are explicitly avoiding the most typical usage of ABC, where the posterior is conditional on summary statistics” this shouldn’t be read as if I am actually claiming that I managed to get around the usage of summary statistics. It’s just that I didn’t want to explicitly consider that additional layer of approximation in the exposition.

But since in some (most) cases usage of summaries is a necessary approach, I guess in a next revision I should emphasize this fact and perhaps point readers to, say, the semi-automatic approach by Fearnhead & Prangle, if not actually using it!

Yes the tuning is repeated at each temperature, in a way that does not necessarily preserve Markovianity *over the whole simulation* but…when tuning is performed — and this happens only in those iterations where the temperature is modified (i.e. the number of clones gets increased) — then we are targeting the posterior corresponding to that specific temperature. So, can’t we just consider the iterations when the tuning is performed (iterations s_1,…,s_q in my notation) as the start of corresponding chains? So the chain produced between iterations (s_j : s_{j+1)} targets the posterior corresponding to that temperature, and so it is consistent with that specific target. When the temperature is increased, the corresponding chain will target the posterior for that specific (modified) temperature and so on…

So I see it as just a possibly very long burn-in to try to approach the final distribution of interest, which is the one with the smallest threshold (delta) and the largest number of clones (K), and once we get there then K and delta are held constant. At this point the long “burn in” has ended and there will be no further adaptation. It is only this last part which is used to produce inferential results (the one without further adaptation), hence it should not cause problem.

I must admit that I don’t quite get the comment on the sentence “This is a so-called “likelihood-free” approach [Sisson and Fan, 2011], meaning that knowledge of the complete expression for the likelihood function is not required.” Could you please clarify further?

Thanks again for the insightful post!

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