Hi Dennis, thanks for taking the time to read and address my insubstantial remarks!!! I understand the fact that using directly a uniform gets back to an earlier stage, but wonder at some potential alternative where the uniforms would be correlated by a copula or something like that, in order to avoid the extra noise due to the cdf estimation, since in theory it should really be a (dependent) uniform.

]]>The idea behind this paper is to try to correct for F_ABC(theta|s) being non-uniform. Assuming it is uniform in our algorithm would simply return the original ABC posterior. But perhaps I’m missing the intention of your remarks…

Regarding the cost, a pure ABC implementation can be expensive. But Scott and Guilherme had a nice idea of speeding up the process using faster estimators for some of the steps – see Section 2.3 of the paper for example. This produces a hybrid method that uses ABC to correct another approximate Bayesian method.

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