  Approximate Bayesian computation (ABC) has become an essential tool for the
analysis of complex stochastic models when the likelihood function is
numerically unavailable. However, the well-established statistical method of
empirical likelihood provides another route to such settings that bypasses
simulations from the model and the choices of the ABC parameters (summary
statistics, distance, tolerance), while being convergent in the number of
observations. Furthermore, bypassing model simulations may lead to significant
time savings in complex models, for instance those found in population
genetics. The BCel algorithm we develop in this paper also provides an
evaluation of its own performance through an associated effective sample size.
The method is illustrated using several examples, including estimation of
standard distributions, time series, and population genetics models.
