Title
Hierarchical processes for spatial extremes
Speaker
Ben Shaby, University of California, Berkeley
Abstract
Economic and social costs brought on by the changing climate are often associated with extreme events like heat waves and intense storms. These events manifestly exhibit spatial dependence. For this reason, models for spatial fields of extreme values are an important tool for assessing risk and devising mitigation strategies. Traditional spatial models based on Gaussian processes are ill-suited to the task because they focus on the center, rather than the tail, of the distribution. In contrast, max-stable processes explicitly model the far tail. Max stable processes are the natural stochastic processes extension of classical univariate extreme value theory, and enjoy a strong theoretical motivation. Unfortunately, known spatial max-stable process models do not possess closed form joint densities, making inference, and in particular Bayesian inference, problematic. Motivated by an agricultural risk assessment application, I describe a way to sidestep this limitation by defining the process hierarchically using a finite-dimensional representation. The resulting process is max-stable, exhibits spatial dependence, has a known spatial max-stable process as a limiting case, and is amenable to true Bayesian analysis via MCMC. Furthermore, the hierarchical framework permits a number of straightforward extensions, including joint modeling of multivariate extreme value fields.
