Approximate Bayesian Computing for Spatial Extremes

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Robert Erhardt*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: Approximate Bayesian Computing ; Likelihood-free ; Extremes ; Max-stable

Abstract

Max-stable processes have become a common choice for modeling spatial extremes. However, closed-form expressions for joint densities are unavailable for any dimension higher than 2. This precludes all inference techniques which require the full likelihood, including traditional Bayesian modeling with MCMC. In this talk, we demonstrate the use of Approximate Bayesian Computing for Spatial Extremes, which only requires simulations from the full joint distribution. Through careful selection of the distance function, proposal density, prior parameter space, and other inputs, one can improve the algorithm and reduce the (admittedly substantial) computational cost. This method is demonstrated using simulations and application to US environmental data, and then compared to the pairwise composite likelihood method.