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Sep 4, 2019 at 2:30 comment added Xi'an There exist MCMC schemes like pseudo-marginal MCMC that are sublinear in the sample size, including some Gibbs implementations using conditionally sufficient statistics. ABC can also be sublinear if one decides to use statistics based on subsamples, including Gibbs versions.
Sep 3, 2019 at 16:13 comment added Dion Thanks for the great reply. I'm trying to draw an analogy with inference on tractable likelihood models using standard MCMC, where each iteration requires a full pass over the dataset, hence linearly scales with dataset size. Replacing the dataset with a "informative subset" of the data in that case would clearly speed up MCMC inference. As per my understanding, this is not the case in likelihood-free inference.
Sep 3, 2019 at 15:02 vote accept Dion
Sep 3, 2019 at 14:31 history answered Xi'an CC BY-SA 4.0