Approximate Bayesian Computing for Spatial Extremes

• Activity Number: 661
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Robert James Erhardt*+ and Richard Smith
• Companies: Wake Forest University and The University of North Carolina at Chapel Hill
• Keywords: max-stable process ; extremal coefficient ; weather risk

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. 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 often results 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 and associated R package ABCExtremes with an application to weather risk data.