Sampling from Max-Stable Processes Conditional on a Homogeneous Functional via an MCMC Algorithm

For managing risks in climate or environmental fields, max-stable processes can be used as models for spatial and spatio-temporal extremes. When some information on the process of interest is available, conditional simulations provide probability distributions according to the information, allowing us to evaluate risks more precisely. Usually the information available is given by observed values of the process in some sites. Instead, in this work, we focus on the case that aggregated data are given. As condition, we consider a homogeneous functional like the integral or the maximum of the process. Due to the analytic intractability of the involved distributions, we propose a sampling algorithm based on MCMC techniques. The procedure consists of two steps where the second step is based on conditional sampling from a max-linear model. We illustrate the performance of the proposed algorithms in a simulation study and in an example of a real dataset of precipitation observations with a condition stemming from regional climate model outputs.