Modelling extremes using approximate Bayesian Computation

TL;DR

This paper explores the use of approximate Bayesian computation (ABC) methods to perform Bayesian inference on extreme value models where likelihood functions are difficult to evaluate, demonstrating applications in stereology and spatial extremes.

Contribution

It introduces ABC techniques specifically tailored for extreme value models and demonstrates their effectiveness in complex spatial and stereological applications.

Findings

ABC methods enable Bayesian inference for intractable extreme models

Successful application to stereology and spatial extremes models

Provides a practical alternative to likelihood-based inference in extreme value analysis

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.