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:<math>\rho (\hat{D},D)\le\epsilon</math>,
where the distance measure <math>\rho(\hat{D},D)</math> determines the level of discrepancy between <math>\hat{D}</math> and <math>D</math> based on a given [[Metric (mathematics)|metric]] (e.g. [[Euclidean distance]]). A strictly positive tolerance is usually necessary, since the probability that the simulation outcome coincides exactly with the data (event <math>\hat{D}=D</math>) is negligible for all but trivial applications of ABC, which would in practice lead to rejection of nearly all sampled parameter points. The outcome of the ABC rejection algorithm is a sample of parameter values approximately distributed according to the desired posterior distribution, and, crucially, obtained without the need to explicitly evaluate the likelihood function.
[[Image:Approximate Bayesian computation conceptual overview.svg|632px|thumb|center|Parameter estimation by approximate Bayesian computation: a conceptual overview.]] ===Summary statistics===
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