ABSTRACT
Abstract 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.
14.1 Introduction Suppose interest is in modelling the extremes of a multivariate random process. A useful example to hold in mind might be measurements of temperature y sampled at locations x1, ..., xD, where there is dependence among the D locations due to their proximity to one another. The extremal dependence may, in general, differ from the dependence of non-extremes, and so the model should target the extremes only and not allow the bulk of non-extreme data to overwhelm the model fit. Models for extremes are useful when trying to estimate the risks associated with rare but influential events.
