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Approximate Bayesian computation (ABC) methods perform inference onmodel-specific parameters of mechanistically motivated parametric statisticalmodels when evaluating likelihoods is difficult. Central to the success of ABCmethods is computationally inexpensive simulation of data sets from theparametric model of interest. However, when simulating data sets from a modelis so computationally expensive that the posterior distribution of parameterscannot be adequately sampled by ABC, inference is not straightforward. Wepresent approximate approximate Bayesian computation" (AABC), a class ofmethods that extends simulation-based inference by ABC to models in whichsimulating data is expensive. In AABC, we first simulate a limited number ofdata sets that is computationally feasible to simulate from the parametricmodel. We use these data sets as fixed background information to inform anon-mechanistic statistical model that approximates the correct parametricmodel and enables efficient simulation of a large number of data sets byBayesian resampling methods. We show that under mild assumptions, the posteriordistribution obtained by AABC converges to the posterior distribution obtainedby ABC, as the number of data sets simulated from the parametric model and thesample size of the observed data set increase simultaneously. We illustrate theperformance of AABC on a population-genetic model of natural selection, as wellas on a model of the admixture history of hybrid populations.

AABC: approximate approximate Bayesian computation when simulating a large number of data sets is computationally infeasible