Approximate Bayesian Computing for Spatial Extremes

TL;DR

This paper introduces an approximate Bayesian computing method for spatial extremes, enabling Bayesian inference without a joint likelihood, and demonstrates its advantages over composite likelihood in terms of accuracy, applied to US temperature data.

Contribution

It presents a novel Bayesian approach using ABC for max-stable processes, overcoming likelihood calculation challenges in spatial extremes modeling.

Findings

ABC achieves lower mean square error than composite likelihood

ABC provides better estimates of spatial dependence in extremes

Method applied successfully to real US temperature data

Abstract

Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper we present a Bayesian approach through the use of approximate Bayesian computing. This circumvents the need for a joint likelihood function by instead relying on simulations from the (unavailable) likelihood. This method is compared with an alternative approach based on the composite likelihood. We demonstrate that approximate Bayesian computing can result in a lower mean square error than the composite likelihood approach when estimating the spatial dependence of extremes, though at an appreciably higher computational cost. We also illustrate the performance of the method with an application to US temperature data to estimate the risk of crop loss due to an unlikely freeze event.