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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