  By the nature of their construction, many statistical models for extremes
result in likelihood functions that are computationally prohibitive to
evaluate. This is consequently problematic for the purposes of likelihood-based
inference. With a focus on the Bayesian framework, this chapter examines the
use of approximate Bayesian computation (ABC) techniques for the fitting and
analysis of statistical models for extremes. After introducing the ideas behind
ABC algorithms and methods, we demonstrate their application to extremal models
in stereology and spatial extremes.
