  Max-stable random fields play a central role in modeling extreme value
phenomena. We obtain an explicit formula for the conditional probability in
general max-linear models, which include a large class of max-stable random
fields. As a consequence, we develop an algorithm for efficient and exact
sampling from the conditional distributions. Our method provides a
computational solution to the prediction problem for spectrally discrete
max-stable random fields. This work offers new tools and a new perspective to
many statistical inference problems for spatial extremes, arising, for example,
in meteorology, geology, and environmental applications.
