  Approximate Bayesian computation (ABC) performs statistical inference for
otherwise intractable probability models by accepting parameter proposals when
corresponding simulated datasets are sufficiently close to the observations.
Producing the large quantity of simulations needed requires considerable
computing time. However, it is often clear before a simulation ends that it is
unpromising: it is likely to produce a poor match or require excessive time.
This paper proposes lazy ABC, an ABC importance sampling algorithm which saves
time by sometimes abandoning such simulations. This makes ABC more scalable to
applications where simulation is expensive. By using a random stopping rule and
appropriate reweighting step, the target distribution is unchanged from that of
standard ABC. Theory and practical methods to tune lazy ABC are presented and
illustrated on a simple epidemic model example. They are also demonstrated on
the computationally demanding spatial extremes application of Erhardt and Smith
(2012), producing efficiency gains, in terms of effective sample size per unit
CPU time, of roughly 3 times for a 20 location dataset, and 8 times for 35
locations.
