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Bayesian inference for spatial extremes, with an application to extreme low temperatures
(Colorado State University)
Models for spatial extremes must account appropriately for asymptotic dependence, and this motivates the use of max-stable processes, which are the only non-trivial limits of properly rescaled pointwise maxima of random functions. The Brown-Resnick max-stable process has proven to be well-suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is unobtainable and inference must be based on a composite likelihood, thereby preventing the use of classical Bayesian techniques. In this talk I will describe a new approach to full likelihood inference for max-stable processes, using componentwise maxima and their partitions in terms of individual events. This approach will be illustrated by the construction of a Bayesian hierarchical model for extreme low temperatures in northern Finland.